Question

Find the value of a and b if 7+5/7-√5-7-√5/7+√5=a+7/11√5b

Answer 1

Solution :

LHS = (7+√5)/(7-√5) - (7-√5)/(7+√5)

= [(7+√5)² - ( 7-√5)²]/[(7-√5)(7+√5)]

= [ 4 × 7 × √5 ]/[ 7² - (√5 )² ]

[ Since , ( a+b)²-(a-b)² = 4ab ]

= 28√5 /( 49 - 5 )

= 28√5 /44

=(7/11)√5

= a + (7/11)√5 b [ Given ]

Therefore ,

0 + (7/11)√5 = a + (7/11)√5 b

Compare both sides, we get

a = 0 , b = 1

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