If m-1-m-5- find the value of m2-1-m2-A- 23B- 5C- 25D- 27

The correct option is A 23 To find the value of ( m^2+1/m^2 ) apply the identity (a+b)^2=a^2+b^2+2ab ⇒ ( m^2+1/m^2 ) = ( m+1/m )^2 2m ×1/m [Here, a=m, b=1/m] ...

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Byju's Answer

Standard VIII

Mathematics

Factorising Expressions of the Form (x+a)(x+b)

If m+1/m=5, f...

Question

If $m + \frac{1}{m} = 5,$ find the value of $m^{2} + \frac{1}{m^{2}} .$

$23$

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$27$

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$5$

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$25$

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Solution

The correct option is A
$23$

To find the value of $(m^{2} + \frac{1}{m^{2}})$ apply the identity $(a + b)^{2} = a^{2} + b^{2} + 2 a b$

$\Rightarrow (m^{2} + \frac{1}{m^{2}}) = {(m + \frac{1}{m})}^{2} - 2 m \times \frac{1}{m}$ [Here, $a = m, b = \frac{1}{m}$ ]

Given, $m + \frac{1}{m} = 5$

Substituting value of $m + \frac{1}{m} = 5$ in the above equation,

We get $m^{2} + \frac{1}{m^{2}} = (5)^{2} - (\frac{2 m}{m})$

$= 25 - 2$ [ $\frac{2 m}{m} = 2$ by cancelling $m$ in numerator and denominator]

$= 23$

Suggest Corrections

If m+1m=5, find the value of m2+1m2.

The correct option is A 23 To find the value of (m2+1m2) apply the identity (a+b)2=a2+b2+2ab ⇒(m2+1m2)=(m+1m)2−2m×1m [Here, a=m,b=1m] Given, m+1m=5 Substituting value of m+1m=5 in the above equation, We get m2+1m2=(5)2−(2mm) =25−2 [2mm=2 by cancelling m in numerator and denominator] =23

If $m + \frac{1}{m} = 5,$ find the value of $m^{2} + \frac{1}{m^{2}} .$