Question

If (x + m) (x + n) = x^2 + 6x + 5 find m^2 + n^2​

Answer 1

Refer to the attachment...

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Answer 2

Concept

A quadratic equation can be factorized by splitting the middle term.

Given

(x + m) (x + n) = x^2 + 6x + 5

Find

we need to find the value of m^2 + n^2​

Solution

We have

(x + m) (x + n) = x^2 + 6x + 5

RHS = x^2 + 6x + 5

Factorizing this equation, we will get

= x^2 + x + 5x + 5

= x(x+1) + 5(x+1)

= (x+1) (x+5)

⇒ (x + m) (x + n) = (x+1) (x+5)

Equating both sides we can infer that

either m = 1 and n = 5

or n = 1 and m = 5

Either ways m^2 + n^2​ will be

5^2 + 1^2

= 25 + 1

= 26

Thus, the value of m^2 + n^2​ is 26.

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