ICSE Class 9 Answered

if sqrt5 -1 / sqrt5 +1 + sqrt5 +1 /sqrt5 -1 = a+ b sqrt5 ; find the values of a and b.

Asked by 011gurmeetdhillon | 06 May, 2020, 04:23: PM

Expert Answer

Given: sqrt5 -1 / sqrt5 +1 + sqrt5 +1 /sqrt5 -1 = a+ b sqrt5

rightwards double arrow fraction numerator square root of 5 minus 1 over denominator square root of 5 plus 1 end fraction plus fraction numerator square root of 5 plus 1 over denominator square root of 5 minus 1 end fraction equals a plus b square root of 5 rightwards double arrow fraction numerator open parentheses square root of 5 minus 1 close parentheses squared over denominator open parentheses square root of 5 plus 1 close parentheses open parentheses square root of 5 minus 1 close parentheses end fraction plus fraction numerator open parentheses square root of 5 plus 1 close parentheses squared over denominator open parentheses square root of 5 plus 1 close parentheses open parentheses square root of 5 minus 1 close parentheses end fraction equals a plus b square root of 5 rightwards double arrow fraction numerator 5 plus 1 minus 2 square root of 5 over denominator 5 minus 1 end fraction plus fraction numerator 5 plus 1 plus 2 square root of 5 over denominator 5 minus 1 end fraction equals a plus b square root of 5 rightwards double arrow fraction numerator 6 minus 2 square root of 5 plus 6 plus 2 square root of 5 over denominator 4 end fraction equals a plus b square root of 5 rightwards double arrow 12 over 4 equals a plus b square root of 5 rightwards double arrow 3 plus 0 square root of 5 equals a plus b square root of 5 H e n c e comma space a equals 3 space a n d space b equals 0.

Answered by Renu Varma | 07 May, 2020, 11:05: AM

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