Question

Solve The equation 4/√ 2 - √5

Answer 1

Solution!!

4/(√2 - √5)

Rationalise the denominator by multiplying.

= 4/(√2 - √5) × (√2 + √5)/(√2 + √5)

= [4(√2 + √5)]/[(√2 - √5)(√2 + √5)]

Simplify the denominator using (a - b)(a + b) = a² - b².

= [4(√2 + √5)]/[(√2)² - (√5)²]

= [4(√2 + √5)]/[2 - 5]

= [4(√2 + √5)]/[-3]

Distribute 4 through the parentheses in the numerator.

= [4√2 + 4√5]/[-3]

We know that - (a/b) = (-a/b) = (a/-b).

= - (4√2 + 4√5)/3

Some more identities:-

→ (a + b)² = a² + b² + 2ab

→ (a - b)² = a² + b² - 2ab

→ (a + b)³ = a³ + b³ + 3ab(a + b)

→ (a - b)³ = a³ - b³ - 3ab(a - b)