Question

if a²+1/a²=34 then find a-1/a​

Answer 1

Answer

a - 1/a = ± 4√2

Given

$\bullet \;\; \rm a^2+\dfrac{1}{a^2}=34$

To Find

$\bullet \;\; \rm a-\dfrac{1}{a}$

Solution

$\rm a^2+\dfrac{1}{a^2}=34\\\\\to \rm \left(a-\dfrac{1}{a}\right)^2+2=34\\\\\to \rm \left(a-\dfrac{1}{a}\right)^2=34-2\\\\\to \rm \left(a-\dfrac{1}{a}\right)^2=32\\\\\to \rm \left(a-\dfrac{1}{a}\right)=\pm \sqrt{32}\\\\\to \rm \left(a-\dfrac{1}{a}\right)=\pm 4\sqrt{2}\ \bigstar$

Answer 2

ANSWER:-

➣

• Given:-

$a^2+ \dfrac{1}{a^2}=34$

• To Find:-

$a-\dfrac{1}{a}$

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• Solution:-

$\longrightarrow{a^2+\dfrac{1}{a^2}=34}$

$\longrightarrow{(a-\dfrac{1}{a})^2+2=34}$

$\longrightarrow{(a-\dfrac{1}{a})^2=34-2}$

$\longrightarrow{(a-\dfrac{1}{a})^2=32}$

$\longrightarrow{(a-\dfrac{1}{a})=\pm \sqrt{32}}$

$\implies(a-\dfrac{1}{a})=\pm 4\sqrt{2}$

Therefore,

$(a-\dfrac{1}{a})\implies {\bf{\pm 4\sqrt{2}}}$

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