Question

if a = √3+√2/√3-√2 and b= √3-√2/√3+√2 find a2+b2
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Answer 1

Step-by-step explanation:

a = (√3+√2)/(√3-√2)

By rationalization,

a = (√3+√2)²/[(√3)²-(√2)²]

a = (3+2+2√6)/(3-2)

a = 5+2√6

a² = (5+2√6)²

a² =25+24 +20√6

a² =49+20√6

____________, _

b = (√3-√2)/(√3+√2)

By rationalization,

b = (√3-√2)²/[(√3)² +(√2)²]

b =(3+2-2√6)/(3+2)

b = (5-2√6)/5

b² = [(5-2√6)/5]²

b² = (25+24-20√6)/25

b² = (49-20√6)/25

________

a²+b² = 49+20√6 +(49-20√6)/5

a²+b² = {5(49+20√6) +49-20√6}/5

a²+b² = (245+100√6 +49-20√6)/5

a²+b² = (245+49 +100√6 -20√6)/5

a²+b² = (294+80√6)/5

a²+b² =16√6 +294/5