1.

If p=√3-√2/√3+√2 and q=√3+√2/√3-√2 then p2+q2​

Answer»

ANSWER:

98

Step-by-step EXPLANATION:

p = √3-√2 ÷ √3+√2

→ √3-√2/√3+√2 × √3-√2/√3-√2

→ (√3-√2)(√3-√2)/(√3+√2)(√3-√2)

→ [√3²+√2²-2(√3)(√2)]/(√3²-√2²)

→ (3+2-2√6)/(3-2)

→ (5-2√6)

q = √3+√2÷√3-√2

→ √3+√2/√3-√2×√3+√2/√3+√2

→ (√3+√2)(√3+√2)/(√3-√2)(√3+√2)

→ [√3²+√2²+2(√3)(√2)]/(√3²-√2²)

→ (3+2+2√6)/(3-2)

→ 5+2√6

⇨p²+q²

⇨ (5-2√6)²+(5+2√6)²

⇨[5²+(2√6)²-2(5)(2√6)] + [5²+(2√6)²+2(5)(2√6)]

⇨(25+4(6)-20√6)+(25+4(6)+20√6)

⇨25+24-20√6+25+24+20√6

⇨49+49

⇨p²+q² = 98

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