Help: 1.\ &x^4-61x^2+900=0 \\ 2. \ & x^4-25x^2+144=0

Question

Help:

`1.\ &x^4-61x^2+900=0 \\ 2. \ & x^4-25x^2+144=0`

Answer 1

`\bf{1) \ x^4-61x^2+900=0 }`

Applying the factorization method, for example:

`\bf{ 0=(x^2)^2-61(x^2)+900=(x^2-36)(x^2-25)}`

`\bf{\\ &=(x+6)(x-6)(x+5)(x-5); }`

`\bf{ x_1=6 \quad x_2=-6 \quad \ \ \ x_3=5 \quad x_4=5 }`

`\bf{2) \ x^4-25x^2+144=0 }`

Applying the factorization method:

`\bf{0&=(x^2)^2-25(x^2)+144=(x^2-16)(x^2-9) }`

`\bf{ =(x-4)(x+4)(x-3)(x+3); }`

`\bf{ x_1=4 \quad x_2=-4 \quad x_3=3 \quad x_4=-3 }`