Question

Hello:) anyone able to explain how to solve the equestrian for part (d) ? Thank youu

Answer 1

see explanation

Explanation:

Given

4
`a^(4)` - 5a² + 1 = 0

Use the substitution u = a², then equation is

4u² - 5u + 1 = 0

Consider the product of the coefficient of the u² term and the constant term

product = 4 × 1 = 4 and sum = - 5

The factors are - 4 and - 1

Use these factors to split the u- term

4u² - 4u - u + 1 = 0 ( factor the first/second and third/fourth terms )

4u(u - 1) - 1(u - 1) = 0 ← factor out (u - 1) from each term

(u - 1)(4u - 1) = 0

Equate each factor to zero and solve for u

u - 1 = 0 ⇒ u = 1

4u - 1 = 0 ⇒ 4u = 1 ⇒ u =
`(1)/(4)`

Convert u back into terms of a, that is

a² = 1 ⇒ a = ± 1

a² =
`(1)/(4)` ⇒ a = ±
`(1)/(2)`

Solutions are a = ± 1 , a = ±
`(1)/(2)`