Question

Two consecutive positive odd integers it turns out that the square of the smaller minus five times the largest is 26 what is the sum of the two integers

Answer 1

The smaller number will be 9 and Larger number will be 11.

Explanation:

Let the smaller odd integer be x.

So the larger odd integer be
`(x+2)`.

The square of the smaller minus five times the largest is 26.

So framing it in equation form, we get;

`x^2-(x+2)5=26\\`

Now Using Distributive property we get;

`x^2-5x-10=26\\`

Now Using Subtraction Property we will Subtract both side by 26 we get

`x^2-5x-10-26=26-26\\x^2-5x-36=0`

Now Factorizing the equation to find the value of x we;

`\\x^2-5x-36=0\\\\x^2-9x+5x-36=0\\\\x(x-9)+5(x-9)=0\\\\(x+5)(x-9)=0\\`

Hence there will be two values of x;

`x+5=0\ \ \ \ and \ \ \ \ x-9=0\\\\x=-5 \ \ \ \ \ \ \ and \ \ \ \ x=9`

Since the Number is a positive Integer hence the value of
`x = 9`

Larger Number=
`x+2=9+2=11`

Hence the smaller number will be 9 and Larger number will be 11.