`a((sqrt(a)+sqrt(b))/(2bsqrt(a)))^(- 1)`+ `b((sqrt(a)+sqrt(b))/(2asqrt(b)))^(- 1)`

If 'a' and 'b' are rational numbers, find the value of a and b in each of the following equations . i) (sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2))=a+bsqrt(6) ii) (sqrt(5)+sqrt(3))/(2sqrt(5)-3sqrt(3))=a-bsqrt(15)

Find the values of a and b in each of the following : (a)(5+2sqrt3)/(7+4sqrt(3))=a-6sqrt(3)" "(b)(3-sqrt(5))/(3+2sqrt(5))=asqrt(5)-(19)/(11) (c )(sqrt(2)+sqrt(3))/(3sqrt2-2sqrt(3))=2-bsqrt(6)" "(d)(7+sqrt(5))/(7-sqrt(5))-(7-sqrt(5))/(7+sqrt(5))=a+(7)/(11)sqrt(5b)

Find the values of a and b in each of the following : (a)(5+2sqrt3)/(7+4sqrt(3))=a-6sqrt(3)" "(b)(3-sqrt(5))/(3+2sqrt(5))=asqrt(5)-(19)/(11) (c )(sqrt(2)+sqrt(3))/(3sqrt2-2sqrt(3))=2-bsqrt(6)" "(d)(7+sqrt(5))/(7-sqrt(5))-(7-sqrt(5))/(7+sqrt(5))=a+(7)/(11)sqrt(5b)

a=(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2)),b=(sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2)) then the value of (1)/(a^(2))+(1)/(b^(2))

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+b sqrt(3)( ii) (3+sqrt(7))/(3-sqrt(7))=a+b sqrt(7)(5+2sqrt(3))/(7+4sqrt(3))=a+b sqrt(3)( iv) (5+sqrt(3))/(7-sqrt(3))=47a+sqrt(3)b(sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))=a+b sqrt(15) (iv) (sqrt(2)+sqrt(3))/(3sqrt(2)-2sqrt(3))=1-b sqrt(3)

If log_((sqrt(bsqrt(bsqrt(bsqrt(b)))))(sqrt(asqrt(asqrt(asqrt(asqrt(a))))))=x log_(b) a , then x =

sqrt(a/b+b/a-2)= 1) sqrt(a/b)+sqrt(b/a) 2) sqrt(a/b)-sqrt(b/a) 3) sqrt(a)/b-b/sqrt(a) 4) sqrt(a)/b-sqrt(b)/a

For (1)/(asqrt(x)+bsqrt(y)) the rationalising factor is a asqrt(x)-bsqrt(y) . If x=(7sqrt(3))/(sqrt(10)+sqrt(3))-(3sqrt(2))/(sqrt(15)+3sqrt(2))-(2sqrt(5))/(sqrt(6)+sqrt(5)) , then value of x^(4)+x^(2) is

Find the value of a and b in each of the following (i)(3+sqrt(2))/(3-sqrt(2))=a+bsqrt(2)" "(ii)(sqrt(2)+1)/(sqrt(2)-1)=a-bsqrt(2)" "(iii)(5+4sqrt(3))/(5-4sqrt(3))=a-bsqrt(3)

Find the value of a and b in each of the following (i)(3+sqrt(2))/(3-sqrt(2))=a+bsqrt(2)" "(ii)(sqrt(2)+1)/(sqrt(2)-1)=a-bsqrt(2)" "(iii)(5+4sqrt(3))/(5-4sqrt(3))=a-bsqrt(3)