Question

a b) If a=0 and a -1 |a= 4; ſind 4 1) a² + 1/a^2? 2) a^4 +1/a^4 ​

Answer 1

Answer:

Step-by-step explanation:

Given that

$a\neq0~\text{and}~ a-\frac{1}{a} = 4$

On squaring both sides of the given equation we get,

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

$or,~a^2 +\frac{1}{a^2} - 2\cdot a\cdot \frac{1}{a} = 16\\or,~a^2 +\frac{1}{a^2} - 2 = 16\\\\or,~a^2 +\frac{1}{a^2} = 16+2\\\\or,a^2+\frac{1}{a^2} = 18$

On squaring both sides of the above equation we get,

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

$or,~a^4+\frac{1}{a^4} + 2\cdot a^2\cdot \frac{1}{a^2} = 324\\or,~a^4+\frac{1}{a^4} + 2 = 324\\or,~a^4+\frac{1}{a^4} = 322$