Question

Find two parts of 20 such that the square
of the greater part exceeds twice the square
of the smaller part by 16. Answers are 8 and 12 , I need explanation​

Answer 1

Solution :

Let 20 be divided into two parts , x and ( 20 - x ) respectively .

[ To simplify and use one variable , u can any variable and it's compliment like x and 20 - x here , but it isn't wrong to take two variables , x and y , or as many as required ]

According to the condition -

The square of the greater part exceeds twice the square of the smaller part by 16.

Let x > 20 - x .

So ,

x² = ( 20 - x )² + 16

=> x² = x² + 400 - 40x + 16

=> 40 x = 416

=> x = 10.4

20 - x = 20 - 10.4 = 9.6

The answer will be 10.4 and 9.6 and not 8 and 12 .

_______________________________________