InterviewSolution
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InterviewSolution
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If both `a`and `b`are rational numbers, find the values of `a`and `b`in each of the following equalities :`(sqrt(3)-1)/(sqrt(3)+1)=a+bsqrt(3)`(ii) `(3+sqrt(7))/(3-sqrt(7))=a+bsqrt(7)``(5+2sqrt(3))/(7+4sqrt(3))=a+bsqrt(3)`(iv) `(5+sqrt(3))/(7-4sqrt(3))=47a+sqrt(3)b``(sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))=a+bsqrt(15)`(iv) `(sqrt(2)+sqrt(3))/(3sqrt(2)-2sqrt(3))=1-bsqrt(3)` |
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Answer» `=(sqrt3-1)/(sqrt3+1)*(sqrt3-1)/(sqrt3-1)` `=(sqrt3-1)^2/(sqrt3^2-1^2)` `=(sqrt3^2+1^2-2sqrt3)/(3-1)` `=(4-2sqrt3)/2` `2-1sqrt3` `a=2,b=-1`. |
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