If-x-1-x-12-find the value of-x-1-x-

X+1/x=12 Squaring on both sides, (x+1/x )^2=(12)^2 ⇒ x^2+1/x^2+2× x^2×1/x^2=144 ⇒ x^2+1/x^2=144 2=142 Now (x 1/x )^2=x^2+1/x^2 2 =142 2=140=4× 35 ∴ x 1/x=√(4× ...

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Standard VIII

Mathematics

Algebraic Identities

If x+1/x=12, ...

Question

$I f x + \frac{1}{x} = 12, find the value of x - \frac{1}{x} .$

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Solution

$x + \frac{1}{x} = 12 Squaring on both sides, {(x + \frac{1}{x})}^{2} = (12)^{2} \Rightarrow x^{2} + \frac{1}{x^{2}} + 2 \times x^{2} \times \frac{1}{x^{2}} = 144 \Rightarrow x^{2} + \frac{1}{x^{2}} = 144 - 2 = 142 N o w {(x - \frac{1}{x})}^{2} = x^{2} + \frac{1}{x^{2}} - 2 = 142 - 2 = 140 = 4 \times 35 ∴ x - \frac{1}{x} = \sqrt[\pm]{4 \times 35} = \pm 2 \sqrt{35}$

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If x+1x=12, find the value of x−1x.

x+1x=12Squaring on both sides,(x+1x)2=(12)2⇒ x2+1x2+2×x2×1x2=144⇒ x2+1x2=144−2=142Now (x−1x)2=x2+1x2−2=142−2=140=4×35∴ x−1x=±√4×35=± 2√35

$I f x + \frac{1}{x} = 12, find the value of x - \frac{1}{x} .$