If x-0 and x-1-2 x-4- then find the value of x2-1-4 x2

The correct option is B 15 Using the identity: (a + b)^2 = nbsp; a^2 + b^2 + 2ab (x + 1/2x)^2 = nbsp;x^2 + 1/4x^2+ 2 × x ×1/2x (x + 1/2x)^2 nbsp;= x^2 + ...

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Byju's Answer

Standard VIII

Mathematics

Algebraic Identity: (a + b)^2 = a^2 + b^2 + 2ab

If x'=0 and x...

Question

If $x \neq 0$ and $x + \frac{1}{2 x}$ = 4, then find the value of $x^{2} + \frac{1}{4 x^{2}}$

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Solution

The correct option is B
15

Using the identity:
$(a + b)^{2} = a^{2} + b^{2} + 2 a b$
$(x + \frac{1}{2 x})^{2}$ = $x^{2} + \frac{1}{4 x^{2}} + 2 \times x \times \frac{1}{2 x}$
$(x + \frac{1}{2 x})^{2}$ $= x^{2} + \frac{1}{4 x^{2}}$ + 1

Substituting the value of $x + \frac{1}{2 x}$ in the above expression we get,
$4^{2}$ $= x^{2} + \frac{1}{4 x^{2}} + 1$
$15 = x^{2} + \frac{1}{4 x^{2}}$

Hence, the value of
$x^{2} + \frac{1}{4 x^{2}} = 15.$

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If x≠0 and x+12x = 4, then find the value of x2+14x2

The correct option is B 15 Using the identity: (a+b)2=a2+b2+2ab (x+12x)2 = x2+14x2+2×x×12x (x+12x)2 =x2+14x2 + 1 Substituting the value of x+12x in the above expression we get, 42 =x2+14x2+1 15=x2+14x2 Hence, the value of x2+14x2=15.

If $x \neq 0$ and $x + \frac{1}{2 x}$ = 4, then find the value of $x^{2} + \frac{1}{4 x^{2}}$