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General Test
Quantitative Reasoning
Algebra
If a=√5+2√5−2 and b=√5−2√5+2, then the value of 2a2+2b2−5ab is equal to : |
693 649 635 639 |
639 |
We know that, (a + b)2 = a2 + b2 + 2ab (a + b)(a – b) = a2 – b2 a=√5+2√5−2 = a = [(√5 + 2)( (√5 + 2)]/[(√5 – 2)(√5 + 2)] = a = [(√5 + 2)2]/[(√5)2 – (2)2] = a = [5 + 4 + 4√5]/(5 – 4) = a = (9 + 4√5) Also, b=√5−2√5+2 = b = [(√5 – 2)(√5 - 2)]/[(√5 + 2)(√5 – 2)] = b = [(√5 – 2)2]/[(√5)2 – (2)2] = b = [5 + 4 – 4√5]/(5 – 4) = b = (9 – 4√5) Now, 2a2+2b2−5ab = 2((9 + 4√5))^2 + 2((9 – 4√5))^2 - 5((9 + 4√5))((9 – 4√5)) = 2(81 + 80 + 72√5) + 2(81 + 80 - 72√5) - 5 = 322 + 322 - 5 = 639 |