solve the equation by making an appropriate substitution x42

solve the equation by making an appropriate substitution x^4-28x^2+75=0

Solution

x^4-28x^2+75=0

Let x^2 =yto make it a quadratic equation:

y^2 -28y +75=0

Factorise:

y^2 -25y -3y +75 =0

y(y-25) -3(y-25) =0

(y-3)(y-25) =0

y =3 and y=25

Now x^2 = 3 ---> x= +sqrt3 , -sqrt3

x^2 = 25 ---> x= 5 , -5

Solution : x= sqrt3, -sqrt3, 5, -5