Question

√2-√4+√8-√16+√32-√64+√128-√256 = a+√b find a+b

Answer 1

Solution:

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i) √4 = 2

ii) √8 = √2×2×2 = 2√2

iii) √16 = √4×4 = 4

iv) √32 = √2×4×4 = 4√2

v) √64 = √8×8 = 8

vi) √128 = √2×8×8 = 8√2

vii) √256 = √16×16 = 16

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Now,

√2-√4+√8-√16+√32-√64+√128-√256 = a+√b

=> √2-2+2√2-4+4√2-8+8√2-16

= a+√b

=> (-2-4-8-16)+(1+2+4+8)√2

= a+√b

=> -30+15√2 = a+√b

Therefore,

a = -30 , b = 2

a+b = -30+2 = -28

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