10th Class Math papers 2025 solution-FBISE-Section B-Q 2-Part vi
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00:00bismillahirrahmanirrahim assalamu alaikum dear students and girls in this class we will cover
00:15the part 6 and subpart a of question number 2 of section b which is related to the 10th class
00:24math paper 205 solution and this paper is belong to the federal board education system so here
00:33is the first part of part 6 of question 2
00:444 parenthesis start 2 raised power 2x plus 1 parenthesis close minus 9 into parenthesis
00:51star 2 raised to power x parenthesis close plus 1 is equal to 0 i have labored this with
00:59equation number 1 solution now i am going to split this factor 4 4 parenthesis star 2 raised power 2x
01:08into 2 2 2 raised power 1 minus 9 parenthesis star into 2 raised power 2x plus 1 is equal to 0
01:22now taking out this 2 and multiply by 4 we will get 8 8 into 2 raised power x
01:29minus square because here is 2x so i will take up to minus 9 into 2x plus 1 is equal to 0
01:42let y is equal to 2 raised power x then 8 y x y square minus 9 y plus 1 is equal to 0
01:50so now i am going to solve this quadratic equation with the help of factorization
02:018 y square multiplied by 1 we will get 8 y square now you have two factors in such a way that when you
02:07multiply it you will get 8 y square positive and you and when you will add up you will get minus 9 y so
02:158 y square minus 8 y minus y when you multiply minus 8 y with minus 5 you will get 8 y square with positive sign
02:24and you will when you will add this minus 8 y minus y you will get minus 9 y so taking out 8 y as a common
02:32factor from this from this so 8 y when they start y minus 1 minus 1 i have taken minus 1 common from
02:40this two elements of the conditions y minus 1 to keep element within the parentheses same 8 y minus 1
02:50into y minus 1 is equal to 0 8 y minus 1 is equal to 0 8 y is equal to 1 and y is equal to 1 by 8 and y
03:01y is equal to 1 now when y when y is equal to 1 then 2x raised to power 1 is equal to
03:07y is equal to 2 x and 1 and y is equal to 1 so 2x raised to power 1 and y is equal to 1 so 2x raised to power 1 is equal to 1
03:21y is equal to 2 x is equal to 2 x is equal to 2 x is equal to 2 raised to power 0 we know that any factor which has power 0 is equal to 1 so base is same on both sides so x is equal to 0
03:35x is equal to 0 now put the value of x in 1 we will get y
03:53bantasy star 2 x is equal to 0 0 plus 1 minus 9 2 raise to power 0 plus 1 and this is equal to
04:100 plus 1 2 4 into 2 minus 9 into 1 plus 1 is equal to 0 8 minus 9 plus 1 is equal to 0 minus 1 plus 1 is
04:19equal to zero zero it means our question is correct notions are now y is equal to 1 by 8
04:272 raised to power x is equal to 1 by 2 1 by 8 2 raised to power x is equal to 1 by 2 raised to
04:33power cube and 2x is equal to 2 raised to power minus 3 and base is same x is equal to minus 3
04:42verification again put the value of x in the equation world we will get this y into
04:503 star 2 raised to power 2 minus 3 plus 1 minus 9 into 2 raised to power minus 3 plus 1 is equal
04:59to 0 4 and 2 princess star 2 into minus 3 minus 6 plus 1 minus 1 by 2 by 3 as the sign is negative
05:09so we will bring it to the denominator with positive sign plus 1 is equal to 0
05:144 by 2 raised to power 5 minus 2 raised to power 3 plus 1 is equal to 0
05:19then 2 5 is here 4 minus 2 3 5 minus 3 2 2 raised to power 2 plus 2 raised to power 5 is equal to 0
05:324 minus 36 plus 32 is equal to 0 is equal to 0 divided by 25 and 36 by 36 36 minus 36 by 25 is equal to 0 0 divided by 2 is equal to 0
05:45now we move to the b part of the part 6 2 x minus 1 x minus divided by x plus 2 raised to power 2 into x minus 6
05:58we have to find the partial fraction so we have to find the partial fraction so 2 x minus 1 divided by x plus 2 raised to power 2 into x minus 3 is equal to a divided by x plus 2 plus b over x plus 2
06:11raised to power 2 plus c over x minus 3 we call it equation a now taking lcm of of right hand side of the equation x plus 2 whole square x minus 3
06:27now come to the here x plus x plus 2 as x plus 2 is cancelled by x plus power 2 only one is remaining x minus 3 plus b into x minus 3 plus c into x plus 2 whole square
06:40x plus 4 x plus 4 x plus 4 x plus 4 x plus 4 x plus 4 x plus 4 x plus 4 x plus 4 x plus 4 x minus 3
06:574 come to this 4 sorry a plus e i have taken common out a x square minus c x square a plus
07:09x square a plus a a plus a a plus c is a coefficient of x here again
07:19minus a plus b and 4 c so this minus is basically tied with this a plus 4 b plus 4 c into x plus into minus 6 a
07:34minus 3 b plus 4 c is equal to minus 3 b plus 4 c is equal to minus 3 by comparing coefficient a plus c is equal to 0
07:44because there is no element x square on the left hand side of the equations minus a plus b plus 4 c is equal to 2
07:53call it equation 2 minus 6 a minus 3 plus plus 4 c is equal to minus 1 call it equation 3
07:59by adding 2 and say we will get minus a plus b plus 4 c is equal to 2
08:11minus 6 a minus 3 b plus 4 c not adding sorry subtracting
08:29subtracting 2 and 3 when we subtract subtracting 2 and 3 when we subtract sign will be changed negative
08:36negative become positive positive become negative so minus turns into positive minus turns into positive
08:43positive positive turns into negative 5 a plus 4 b and 4 c is cancelled by minus 4 c is equal to
08:51negative minus minus 1 turn into plus plus is equal to 3 multiplying equation 1 by 4 and subtract from 2
09:01minus a plus b plus 4 c is equal to 2 minus 4 a plus 0 b as there is no element of b plus 4 c is equal to 0
09:11and this positive turn into minus and plus into negative plus into negative minus 5 a plus b is equal to 2
09:24by adding 4 and 5 5 a plus 4 b is equal to 3 minus 5 a plus b is equal to 2 5 b is equal to 5 and b is equal to 1
09:35by putting value of b in equation 5 minus 5 a plus 1 is equal to 2 minus 5 a is equal to 2 minus 1 and minus 5 a is equal to 1 and a is equal to minus 5 now
09:50put value of a in equation 1 minus 1 by 5 plus c is equal to c is equal to 0 c is equal to 1 by 5
09:59by putting value of a b and c in 1 minus 1 by 5 x plus 2 plus 1 divided by x plus 2 whole square plus 1 by 5 x minus 3 verification
10:19taking lcm of both sides 5 into x plus 2 whole square into x minus 3 minus x plus 2
10:26x minus 2 x plus 2 x plus 2 x plus 2 x plus 5 x minus 15 plus x square plus 4 x plus 4 x plus 4
10:45minus x square minus x minus 6 5 x minus 15 x square plus 4 x plus 4 divided by 5 into x plus 2 whole square
10:54x minus 2 x minus 2 x minus 2 x minus 2 x minus 2 x minus 2 x minus 3 look at this minus x square is
10:59considered out by x square minus x square plus x plus 6 plus 5 x minus 15 x square plus 4 x plus 4 this is
11:12x square minus 5 x plus 5 x plus 5 x plus 5 x plus 5 x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x plus x
11:425 into x plus 2 whole square x minus 3, taken 5 common out of the numerator 2x minus 1 and 5 is cancelled by 5, 5 thus 2x minus 1 divided by x plus 2 whole square x minus 3 is equal to 2x minus 1 divided by x plus 2 whole square x minus 3, left hand side is equal to right hand side, the master rate values of a, b and c are correct.
12:10Thanks for watching, assalamu alaikum, if you have any query you can ask me in the comment section or maybe.
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