Question

find a and b if 2 root 5 + root 3 / 2 root 5 minus root 3 + 2 root 5 minus root 3 / 2 root 5 + root 3 is equal to a + root 15 b​

Answer 1

Solution :-

Solving LHS,

→ {(2√5 + √3)/(2√5 - √3)} + {(2√5 - √3)/(2√5 + √3)}

taking LCM,

→ {(2√5 + √3)² + (2√5 - √3)²} / {(2√5 - √3)(2√5 + √3)}

→ (20 + 3 + 4√15 + 20 + 3 - 4√15) / (20 - 3)

→ (46/17)

now, putting LHS = RHS,

→ (46/17) = a + b√15

→ (46/17) + 0√15 = a + b√15

comparing we get,

• a = (46/17) .
• b = 0 .

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Answer 2

Answer:

Solving LHS,

→ {(2√5 + √3)/(2√5 - √3)} + {(2√5 - √3)/(2√5 + √3)}

taking LCM,

→ {(2√5 + √3)² + (2√5 - √3)²} / {(2√5 - √3)(2√5 + √3)}

→ (20 + 3 + 4√15 + 20 + 3 - 4√15) / (20 - 3)

→ (46/17)

now, putting LHS = RHS,

→ (46/17) = a + b√15

→ (46/17) + 0√15 = a + b√15

comparing we get,

a = (46/17) .

b = 0 .

Step-by-step explanation: