Question

Prove that (3√2-2√3/3√2+2√3) +(2√3/√3-√2) =11

Answer 1

Answer:

L.H.S = R.H.S

Step-by-step explanation:

We have to show that

((3√2-2√3)/(3√2+2√3)) + (2√3/(√3-√2)) = 11

L.H.S = ((3√2-2√3)/(3√2+2√3)) + (2√3/(√3-√2))

By rationalization we get

=((3√2-2√3)/(3√2+2√3))((3√2-2√3)/(3√2-2√3)) + (2√3/(√3-√2))((√3+√2)/(√3+√2))

= (3√2-2√3)² / (9(2) - 4(3)) +  ((2√3)(√3+√2)) / (3 - 2)

= (( 18 + 12 - 12√6 ) / (18 - 12)) + ( 2(3) + 2√6 ) / 1

= (( 30 - 12√6) / 6 )  +  6 + 2√6

= 5 - 2√6 + 6 + 2√6

= 11

= R.H.S

Hence

L.H.S = R.H.S

Answer 2

Step-by-step explanation:

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