Question

if a= √3+√2/√3-√2 and b= √3-√2/√3+√2 find a^3 + b^3​

Answer 1

Answer:

98

Step-by-step explanation:

a = (√3+√2)/(√3-√2)

By rationalization,

a = (√3 + √2)/(√3 - √2) ×(√3+√2)/(√3+√2)

a = (√3+√2)² / (√3)²-(√2)² )

a = (3+2+2√6)/(3-2) = 5 + 2√6

Therefore,

a² = (5+2√6)²

a² =49+20√6

___________, _

b = (√3-√2)/(√3+√2)

By rationalization,

b = (√3-√2)/(√3+√2)× (√3 - √2)/(√3 - √2)

b = (√3-√2)² / ((√3)² - (√2)² )

b =(3+2-2√6)/(3-2) = 5 - 2√6

Therefore,

b² = (5 - 2√6)²

b² = 49 - 20√6

________

a²+b² = 49+20√6 + 49-20√6

a² + b² = 98