Question

if a-1/a=5 find the value of a^2+1/a^2​

Answer 1

$\huge\bold{\mathtt{Question⇒}}$

If $a-{\frac{1}{a}}=5$, find the value of $a²+{\frac{1}{a²}}$.

$\huge\bold{\mathtt{Given⇒}}$

$a-{\frac{1}{a}}=5$

$\huge\bold{\mathtt{To\:find⇒}}$

The value of $a²+{\frac{1}{a²}}$.

$(a-b)²=a²+b²-2ab$

$\huge\bold{\mathtt{Solution⇒}}$

We know that:

$\large{\boxed{(a-b)²=a²+b²-2ab}}$

$∴\:a-{\frac{1}{a}}=5$

Square both the sides.

$➳\:(a-{\frac{1}{a}})²=(5)²$

$➳\:a²+({\frac{1}{a}})²-2×a×{\frac{1}{a}}=25$

$➳\:a²+{\frac{1}{a²}}-2×\cancel{a}×{\frac{1}{\cancel{a}}}=25$

$➳\:a²+{\frac{1}{a²}}-2=25$

Add $2$ to both sides.

$➳\:a²+{\frac{1}{a²}}-2+2=25+2$

$➳\:a²+{\frac{1}{a²}}\:\cancel{-2}\:\cancel{+2}=27$

$➳\:a²+{\frac{1}{a²}}=27$

$\huge\bold{\mathtt{Hence⇒}}$

$a²+{\frac{1}{a²}}=27$

$\huge\bold{\mathtt{Therefore⇒}}$

The value of $a²+{\frac{1}{a²}}$ is $27.$

$\huge\bold{\mathtt{Done࿐}}$

$\large\bold{\mathtt{Hope\:this\:helps\:you.}}$

$\large\bold{\mathtt{Have\:a\:nice\:day.}}$