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Construct a word problem on quadratic eq...

Construct a word problem on quadratic equation, such that one of its answers is 6 ( years, natural numbers, rupees, etc. ) Also solve it.
Word problem `:`
The difference between two positive integers is 4 and the sum of their squares is 40 . Find the greater number.

Text Solution

Verified by Experts

The correct Answer is:
The greater number is 6.
Let the greater number be x.
From the first condition , the smaller numer is x-4 .
From the second condition, `x^(2) + ( x-4)^(2) = 40`
`:. x^(2) + x^(2) - 8 x+ 16 = 40 `
`:. 2x^(2) - 8x+ 16 - 40 = 0 ` `:. 2x^(2) - 8x- 24 = 0 `
`:. x^(2) - 4x - 12=0` ....(Dividing by 2 )
`:. x^(2) - 6 x + 2 x - 12 = 0 `
`:. x( x-6) + 2(x-6) = 0 ` `:. ( x-6) ( x+2) = 0 `
`:. x - 6 = 0` or `x+2=0` `:. x = 6 ` or `x = - 2 `
`x = - 2 ` is unacceptable `:'` It is not a positive integer
`:. x= 6 `
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