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मान लिया कि `a=sqrt(6)-sqrt(5),b=sqrt(5)-2,c=2-sqrt(3)` है तो निम्न विकल्पों में से कौन सा विकल्प सही है?A. `b lt a lt c`B. `a lt c lt b`C. `b lt c lt a`D. `a lt b lt c` |
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Answer» Correct Answer - D `a=sqrt(6)-sqrt(5)` `b=sqrt(5)-2` `c=2-sqrt(3)` Rationalize all the terms `a=(sqrt(6)-sqrt(5))/(sqrt(6)+sqrt(5))xxsqrt(6)+sqrt(5)` `=1/(sqrt(6)+sqrt(5))` `b=(sqrt(5)-2)/(sqrt(5)+2)xxsqrt(5)+2=1/(sqrt(5)+2)` `=1/(sqrt(5)+sqrt(4))` `c=(2-sqrt(3))/(2+sqrt(3))xx 2+sqrt(3)` `=1/(2+sqrt(3))=1/(sqrt(4)+sqrt(3))` NOw, `a=1/(sqrt(6)+sqrt(5))` `b=1/(sqrt(5)+sqrt(4))` `c=1/(sqrt(4)+sqrt(3))` Now the term whose denominator is largest is the smallest term. So `altbltc`. |
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