determine all the values of y that satisfy the equation y^4-13y^2+36=0

Answer 1

To determine all the values of y that satisfy the equation y^4 - 13y^2 + 36 = 0, we can treat it as a quadratic equation by letting z = y^2.

Substituting z into the equation, we have z^2 - 13z + 36 = 0.

Now, we can solve this quadratic equation for z. Factoring it, we have (z - 4)(z - 9) = 0.

Setting each factor equal to zero, we get z - 4 = 0 and z - 9 = 0.

Solving each equation, we find that z = 4 and z = 9.

Substituting back y^2 in place of z, we can solve for y:
For z = 4:
y^2 = 4
y = ±2

For z = 9:
y^2 = 9
y = ±3

Thus, all the values of y that satisfy the equation y^4 - 13y^2 + 36 = 0 are y = ±2 and y = ±3.