Solve 9/8+b^2+1/b^2=1

$$\frac { 9 } { 8 + b ^ { 2 } } + \frac { 1 } { b ^ { 2 } } = 1$$

Solve for b

$$b=2$$

$$b=-2$$

Steps Using the Quadratic Formula

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by b^{2}\left(b^{2}+8\right), the least common multiple of 8+b^{2},b^{2}.

$$b^{2}\times 9+b^{2}+8=b^{2}\left(b^{2}+8\right)$$

Combine b^{2}\times 9 and b^{2} to get 10b^{2}.

$$10b^{2}+8=b^{2}\left(b^{2}+8\right)$$

Use the distributive property to multiply b^{2} by b^{2}+8.

$$10b^{2}+8=b^{4}+8b^{2}$$

Subtract b^{4} from both sides.

$$10b^{2}+8-b^{4}=8b^{2}$$

Subtract 8b^{2} from both sides.

$$10b^{2}+8-b^{4}-8b^{2}=0$$

Combine 10b^{2} and -8b^{2} to get 2b^{2}.

$$2b^{2}+8-b^{4}=0$$

Substitute t for b^{2}.

$$-t^{2}+2t+8=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute -1 for a, 2 for b, and 8 for c in the quadratic formula.

$$t=\frac{-2±\sqrt{2^{2}-4\left(-1\right)\times 8}}{-2}$$

Do the calculations.

$$t=\frac{-2±6}{-2}$$

Solve the equation t=\frac{-2±6}{-2} when ± is plus and when ± is minus.

$$t=-2 t=4$$

Since b=t^{2}, the solutions are obtained by evaluating b=±\sqrt{t} for positive t.

$$b=2 b=-2$$