Question
$12/{3 + √5 + 2√2}$ is equal to
Answer: Option D
Answer: (d)Expression= $12/{3 + √5 + 2√2}$= ${12(3+√5-2√2)}/{[(3+√5)+2√2][(3+√5)-2√2]}$[Rationalising the denominator]= ${12(3+√5-2√2)}/{(3+√5)^2- (2√2)^2}$= ${12(3+√5-2√2)}/{9+5+6√5-8}$= ${12(3√5-2√2)}/{6√5+6}$= ${2(3+√5-2√2)}/{√5+1}$= ${2(3+√5-2√2)(√5-1)}/{(√5+1)(√5-1)}$= ${2(3√5+5-2√{10}-3-√5+2√2)}/{5-1}$= ${2(2√5+2√2-2√{10}+2)}/4$= ${2×2(√5+√2-√{10}+1)}/4$= $1+√5+√2-√{10}$
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Answer: (d)Expression= $12/{3 + √5 + 2√2}$= ${12(3+√5-2√2)}/{[(3+√5)+2√2][(3+√5)-2√2]}$[Rationalising the denominator]= ${12(3+√5-2√2)}/{(3+√5)^2- (2√2)^2}$= ${12(3+√5-2√2)}/{9+5+6√5-8}$= ${12(3√5-2√2)}/{6√5+6}$= ${2(3+√5-2√2)}/{√5+1}$= ${2(3+√5-2√2)(√5-1)}/{(√5+1)(√5-1)}$= ${2(3√5+5-2√{10}-3-√5+2√2)}/{5-1}$= ${2(2√5+2√2-2√{10}+2)}/4$= ${2×2(√5+√2-√{10}+1)}/4$= $1+√5+√2-√{10}$
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