Question

a+1/a=4 then a4+1/a4=?
?​

Answer 1

Answer:

first notist that (a+1/a)2=42=16.

but also, (a+1/a2=a2

Answer 2

Answer:

$a + \frac{1}{a} = 4 \\ squaring \: on \: both \: sides \\ (a + \frac{1}{a} ) ^{2} = 4 ^{2} \\ a^{2} + \frac{1}{{a}^{2} } + 2 = 16 \\ a^{2} + \frac{1}{{a}^{2} } = 16 - 2 \\ a^{2} + \frac{1}{{a}^{2} } = 14 \\ squaring \: on \: both \: sides \\ (a^{2} + \frac{1}{{a}^{2} } ) ^{2} = 14^{2} \\ {a}^{4} + \frac{1}{a ^{4} } + 2 = 196 \\ {a}^{4} + \frac{1}{a ^{4} } = 196 - 2 \\ {a}^{4} + \frac{1}{a ^{4} } = 194$

Remember:

(a+b)²= a²+b²+2ab