fraction numerator 5 plus square root of 11 over denominator 3 minus 2 square root of 11 end fraction equals x plus y square root of 11

Asked by jjain3888 | 12th Sep, 2020, 08:03: AM

Expert Answer:

Given: (5 + sqrt{11})/(3 - 2 sqrt{11}) = x + ysqrt{11}
To find x and y
fraction numerator 5 plus square root of 11 over denominator 3 minus 2 square root of 11 end fraction equals fraction numerator 5 plus square root of 11 over denominator 3 minus 2 square root of 11 end fraction cross times fraction numerator 3 plus 2 square root of 11 over denominator 3 plus 2 square root of 11 end fraction equals fraction numerator 15 plus 10 square root of 11 plus 3 square root of 11 plus 2 cross times 11 over denominator 9 minus 4 cross times 11 end fraction equals fraction numerator 37 plus 13 square root of 11 over denominator negative 35 end fraction equals negative 37 over 35 minus 13 over 35 square root of 11
rightwards double arrow negative 37 over 35 minus 13 over 35 square root of 11 equals space straight x plus straight y square root of 11
rightwards double arrow straight x equals negative 37 over 35 space and space straight y equals negative 13 over 35

Answered by Renu Varma | 14th Sep, 2020, 11:30: AM