If $(x^{2} + 3 x + 5) (x^{2} - 3 x + 5) = m^{2} - n^{2}$ , then $m =$ ________.

x^{2} - 3 x

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3 x

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x^{2} + 5

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Both

(A)

and

(B)

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Solution

The correct option is C $x^{2} + 5$
Given : $(x^{2} + 3 x + 5) (x^{2} - 3 x + 5) =$ $m^{2} - n^{2}$
We know that, $m^{2} - n^{2} = (m + n) (m - n)$ $[Identity]$
We can write above equation as,
$\Rightarrow$ $(x^{2} + 3 x + 5) (x^{2} - 3 x + 5) = ((x^{2} + 5) + 3 x) ((x^{2} + 5) - 3 x)$
$\Rightarrow$ $(x^{2} + 3 x + 5) (x^{2} - 3 x + 5) = (x^{2} + 5)^{2} - (3 x)^{2}$
Therefore, $m = x^{2} + 5$ and $n = 3 x$

Suggest Corrections

Similar questions

The factors of x⁴ + x² + 25 are

(a) (x² + 3x + 5) (x² − 3x + 5)

(b) (x²+ 3x + 5) (x² + 3x − 5)

(c) (x² + x +5) (x² − x + 5)

(d) none of these

(x^{2} - 3 x)^{2} - 5 (x^{2} + 3 x) - y (x^{2} + 3 x) + 5 y

= (x^{2} + 3 x - 5) (x^{2} + 3 x - y)

x^{2} - 3 x + 10 = 0

x^{2} - 3 x - 10 = 0

x^{2} + 3 x - 10 = 0

x^{2} + 3 x + 10 = 0

^{2}

^{2}

^{2}

A = 2 y^{2} + 3 x - x^{2}, B = 3 x^{2} - y^{2}

C = 5 x^{2} - 3 x y

A + B

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