Question

3/√3-√2=a√3-b√2 Find value of a & b​

Answer 1

Answer:

= a²+b²

= [(√3+√2)/(√3-√2)]² + [(√3-√2)/(√3+√2)]²

= (√3+√2)²/(√3-√2)² + (√3-√2)²/(√3+√2)² [b/z, (a/b)² = a²/b²]

= [(√3)²+2(√3)(√2)+(√2)²]/[(√3)²-2(√3)(√2)+(√2)²] + [(√3)²-2(√3)(√2)+(√2)²]/[(√3)²+2(√3)(√2)+(√2)²] [b/z, (a+b)²=(a²+2ab+b²) & (a-b)²=(a²-2ab+b²)]

= (3+2√6+2)/(3–2√6+2)+(3–2√6+2)/(3+2√6+2)

= (5+2√6)/(5–2√6)+(5–2√6)/(5+2√6)

Now, take LCM,

= [(5+2√6)(5+2√6)+(5–2√6)(5–2√6)]/(5–2√6)(5+2√6)

= [(5+2√6)²+(5–2√6)²]/(5)²-(2√6)²

= {[(5)²+2(5)(2√6)+(2√6)²]+[(5)²-2(5)(2√6)+(2√6)²]}/25–4(√6)(√6)

= [(25+20√6+24)+(25–20√6+24)]/25–24

= (49+20√6+49–20√6)/ 1

= 98/1

= 98

Step-by-step explanation:

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