Solve y=64k^4-(3+4k^2)(34k^2-12)

$$y = 64 k ^ { 4 } - ( 3 + 4 k ^ { 2 } ) ( 34 k ^ { 2 } - 12 )$$

Solve for y

$$y=36-54k^{2}-72k^{4}$$

Solution Steps

Use the distributive property to multiply 3+4k^{2} by 34k^{2}-12 and combine like terms.

$$y=64k^{4}-\left(54k^{2}-36+136k^{4}\right)$$

To find the opposite of 54k^{2}-36+136k^{4}, find the opposite of each term.

$$y=64k^{4}-54k^{2}+36-136k^{4}$$

Combine 64k^{4} and -136k^{4} to get -72k^{4}.

$$y=-72k^{4}-54k^{2}+36$$

Solve for k (complex solution)

$$k=\frac{\sqrt{-6\sqrt{369-8y}-54}}{12}$$

$$k=-\frac{\sqrt{-6\sqrt{369-8y}-54}}{12}$$

$$k=-\frac{\sqrt{6\sqrt{369-8y}-54}}{12}$$

$$k=\frac{\sqrt{6\sqrt{369-8y}-54}}{12}$$

Solve for k

$$k=-\frac{\sqrt{6\left(\sqrt{369-8y}-9\right)}}{12}$$

$$k=\frac{\sqrt{6\left(\sqrt{369-8y}-9\right)}}{12}\text{, }y\leq 36$$