Question

if a + 1\a = 11 find the value of a square + 1 by a square

Answer 1

$a + \frac{1}{a} = 11 \\ squaring \: both \: sides \\ {a}^{2} + { \frac{1}{a} }^{2} = {11}^{2} \\ = {a}^{2} + \frac{1}{ {a}^{2} } + 2 \times a \times \frac{1}{a} = 121 \\ = {a}^{2} + \frac{1}{ {a}^{2} } + 2 = 121 \\ = {a}^{2} + \frac{1}{ {a}^{2} } = 121 - 2 = 119$

Answer 2

Answer:

\begin{gathered}a + \frac{1}{a} = 11 \\ squaring \: both \: sides \\ {a}^{2} + { \frac{1}{a} }^{2} = {11}^{2} \\ = {a}^{2} + \frac{1}{ {a}^{2} } + 2 \times a \times \frac{1}{a} = 121 \\ = {a}^{2} + \frac{1}{ {a}^{2} } + 2 = 121 \\ = {a}^{2} + \frac{1}{ {a}^{2} } = 121 - 2 = 119 \end{gathered}

a+

a

1

=11

squaringbothsides

a

2

+

a

1

2

=11

2

=a

2

+

a

2

1

+2×a×

a

1

=121

=a

2

+

a

2

1

+2=121

=a

2

+

a

2

1

=121−2=119