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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

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Answer:

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.

User Yanos
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