Question

If x=2√6\√3+√2
then find
x+√2\x-√2+x+√3\x-√3
​

Answer 1

Answer:

X = (2√6)/(√3 +√2)

x +√2 = 2√6/(√3+√2) +√2

=(2√6 +√6 +2)/(√3 +√2)

=(3√6+2)/(√3+√2)

x-√2 =(2√6 -√6-2)

=(√6 -2)

(x +√2)/(x-√2) = (3√6+2)/(√6-2)

again,

(x +√3) =(2√6 +3+√6)

=(3√6+3)

(x-√3)=(2√6-3-√6)

=(√6-3)

(x+√3)/(x-√3) =(3√6+3)/(√6-3)

(x +√2)/(x -√2) +(x +√3)/(x -√3)

=(3√6+2)/(√6-2)+ (3√6+3)/(√6-3)

={18 +2√6 -9√6-6+18+3√6-6√6-6}/(√6-2)(√6-3)

={36-12 -10√6}/(6-5√6+6)

=(24-10√6)/(12-5√6)

=2 (answer)

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