Find the value of ‘a’ and ‘b’ if 7+3√53 + √5 - 7−3√53 − √5 = a + √5b
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Step-by-step explanation:
What is the value of a and b ((7+3√5) / (2+√5)-(7-3√5) / (2-√5) =a+b√5?
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4 Answers
Samadrita Saha
Answered February 9, 2018
7+3√52+√5−7−3√52−√57+3√52+√5−7−3√52−√5
=(7+4√5)(2−√5)−(7−3√5)(2+√5)(2+√5)(2−√5)=(7+4√5)(2−√5)−(7−3√5)(2+√5)(2+√5)(2−√5)
=14−7√5+6√5−15−14−7√5+6√5+154−5=14−7√5+6√5−15−14−7√5+6√5+154−5
=−14√5+12√5−1=−14√5+12√5−1
=2√5=2√5
Comparing LHS and RHS,
a=0a=0 and b=2.b=2.
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Ved Prakash Sharma, former Lecturer at Sbm Inter College, Rishikesh (1971-2007)
Answered February 16, 2018
(7+3.5^1/2)/(2+5^1/2) - (7–3.5^1/2)/(2–5^1/2)=a+b.5^1/2
or {(7+3.5^1/2)/(2+5^1/2)}×{(2–5^1/2)/(2–5^1/2)}-{(7–3.5^1/2)/(2–5^1/2)}×{(2+5^1/2)/(2+5^1/2)}=a+b.5^1/2
or (14+6.5^1/2–7.5^1/2–15)/(-1)-(14–6.5^1/2+7.5^1/2–15)/(-1)=a+b.5^1/2
or (1+5^1/2)+(-1+5^1/2)=a+b.5^1/2
or 0+2.5^1/2=a+b.5^1/2 , equating both side
a=0 , b =2 , Answer