00:00Okay, in this question, is the following situation possible?
00:07If so, determine the present age.
00:11Now the question is, the sum of the age of 2 friends is 20 years, not the present sum.
00:17Okay, friend 1 and our friend 2.
00:20So this is our friend 1 and this is my friend 2.
00:25Okay, the age of 2 friend, the sum of the age of 2 friend is 20 years.
00:32If x here is the age of friend 1, then what is the age of friend 2?
00:40It is 20 minus x. What? 20 minus x.
00:45Okay, 4 years ago, 4 years ago, what is the age?
00:50x minus 4 and age is 20 minus x minus 4.
00:58Okay, now 20 minus x minus 4 is equal to what? 16 minus x years.
01:04Okay, so the friend 1 age is x minus 4 years and friend 2 age is 16 minus x years.
01:15Now what is given? The product. And what is the product? 48.
01:19Product is given? 48 years.
01:22So x minus 4, x minus 4, second bracket, 16 minus x is equal to 48 years. Okay, 48.
01:34Now, we have to find this given situation is possible or not.
01:40So we have to solve this question. Okay.
01:44Now, we have x into 16 that is 16x minus x into x that is x square minus 16 into 4, 64.
02:064 into x minus 4 minus x plus 4 x is equal to 48. Okay.
02:19Now, taking all these values. Now, taking all these values, one side, we have 16 plus 4, that is 20, and minus x square, putting the value minus x square, very first, plus 16x plus 4x is equal to 20x, minus 64 minus 48 is equal to 0.
02:47Therefore, we have, if we have, if we have, multiply with minus 1, both sides, then minus 1 into 0 is equal to 0.
02:56And minus 1 into minus 1 into minus x square is equal to x square minus 20x plus 1, 1, 2. Okay.
03:13Because this is negative, because this is negative, because this is negative, and when we multiply both with minus 1, it becomes positive and is equal to 0.
03:21Now, comparing these with a square minus bx, a square plus bx plus c, we have, a x square plus bx plus c is equal to 0, then a is equal to 1, b is equal to minus 20, and c is equal to 112. Okay.
03:44Now, what is the value of b square minus 4ac? Because if b square minus 4ac is equal to 0, or is greater than 0, then we have real root.
03:53Okay. So, b square minus 4ac is equal to what? b square is equal to minus 20 square minus 4 into 1 into 112.
04:08That is, 20 into 20, that is, 20 into 20, 400, minus minus, plus, minus, 4 to the 8, 4 1 into 4, and 4 1 into 4, is equal to minus 48.
04:23So, we have answer minus 48, b square minus 4ac, that's, discriminant is negative, so no real root can be found.
04:32Okay. So, our answer is, no real root present. So, there is no answer, or this equation is not proper.
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