(i) Given x^{4} – 26x^{2} + 25 = 0
Putting, x^{2 }= y, the given equation reduces to the form y^{2} – 26y + 25 = 0
⇒ y^{2} – 25y – y + 25 = 0
⇒ y(y – 25) – 1(y – 25) = 0
⇒ (y – 25)(y – 1) = 0
⇒ y – 25 = 0 or y – 1 = 0
⇒ y = 25 or y = 1
∴ x^{2} = 25
⇒ x = ± 5
or x^{2} = 1
x = ± 1
Hence, the required roots are ± 5, ± 1.
(ii) Given equation z^{4} – 10z^{2} + 9 = 0
Putting z^{2} = x, then given equation reduces to the form x^{2} – 10x + 9 = 0
⇒ x^{2} – 9x – x + 9 = 0
⇒ x(x – 9) – 1(x – 9) = 0
⇒ (x – 9)(x – 1) = 0
⇒ x – 9 = 0 or x – 1 = 1
⇒ x = 9 or x = 1
But z^{2} = x
∴ z^{2} = 9
⇒ z = ± 3
Or z^{2} = 1
z = ± 1
Hence, the required roots are ± 3, ± 1.