Question

If a³-102a +209 =0, then find the value of (a-2)²+1/(a-6)²​

Answer 1

Given:

a³-102a +209 =0

To find:

(a-2)²+1/(a-6)²​ =?

Step-by-step explanation:

a³-102a +209 =0

a ( $a^2$ -102 ) = -209

By solving above eq we get the values of a:

a = - 11     a = 8.85     a = 2.14

Now we have to find the value of

    (a-2)²+$\frac{1}{(a - 6)^2}$    ...(1)

1)

for a = -11

put this in eq (1)

(a-2)² + $\frac{1}{\displaystyle (a - 6)^2}$= $\displaystyle ( -11 -2)^2 + \frac{1}{( -11 -6)^2}$

                     = - 169.00

2)

for a = 8.85

put this in eq (1)

(a-2)² + $\frac{1}{\displaystyle (a - 6)^2}$ = $\displaystyle ( 8.85 -2)^2 + \frac{1}{(8.85 -6)^2}$

                          = 47.04

3)

for a = 2.14

put this in eq (1)

(a-2)² +$\frac{1}{\displaystyle (a - 6)^2}$  = $\displaystyle ( 2.14 -2)^2 + \frac{1}{(2.14 -6)^2}$

                          = - 0.0475