Question

if a-1/a=4,find the value of a²+1/a²

Answer 1

See the attached file

Answer 2

Answer:

$The \: value \: of\\ \: a^{2}+\frac{1}{a^{2}}= 18$

Step-by-step explanation:

$We \: have \: a -\frac{1}{a}=4---(1)$

$On \: Squaring \: the \: equation \: (1),\\ \: we \: get$

$(a-\frac{1}{a})^{2}=4^{2}$

$\implies a^{2}+\frac{1}{a^{2}}-2\times a\times \frac{1}{a} = 16$

/* By algebraic identity:

$\boxed {(x-y)^{2}=x^{2}+y^{2}-2xy}$*/

$\implies a^{2}+\frac{1}{a^{2}}-2 = 16$

$\implies a^{2}+\frac{1}{a^{2}} = 16+2$

$\implies a^{2}+\frac{1}{a^{2}} = 18$

Therefore,

$The \: value \: of\\ \: a^{2}+\frac{1}{a^{2}} = 18$

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