`(sqrt3 + sqrt7)^2` and `(5+sqrt7)(2+sqrt5)`

If x= ( sqrt5- sqrt3)/ ( sqrt5+ sqrt3) and y= ( sqrt5+ sqrt3)/( sqrt5- sqrt3) find the value of x^(2) + y ^(2)

(3-sqrt7)(3+sqrt7)=?

Find the number of terms in the following expansions. ( sqrt(3) + sqrt(5) )^(7) ( sqrt(3) - sqrt(5) )^(7)

Simplify the following expressions: (i)\ (sqrt(3)+\ sqrt(7))^2 (ii)\ (sqrt(5)-sqrt(3))^2 (iii)\ (2sqrt(5)+3sqrt(2))^2

If x=(sqrt(5)+\ sqrt(3))/(sqrt(5)-\ sqrt(3)) and y=(sqrt(5)-\ sqrt(3))/(sqrt(5)+\ sqrt(3)) , then x+y+x y= (a) 9 (b) 5 (c) 17 (d) 7

Simplify the following expressions. (i) (5+sqrt(7))(2+sqrt(5)) (ii) (5+sqrt(5))(5-sqrt(5)) (iii) (sqrt(3)+sqrt(7))^2 (iv) (sqrt(11)-sqrt(7))(sqrt(11)+sqrt(7))

Simplify the following expressions: (i) (sqrt(3)+sqrt(7))^2 (ii) (2sqrt(5)+3sqrt(2))^2

{:(sqrt(5)x - sqrt(7)y = 0),(sqrt(7)x - sqrt(3)y = 0):}

The abscissas of point Pa n dQ on the curve y=e^x+e^(-x) such that tangents at Pa n dQ make 60^0 with the x-axis are. 1n((sqrt(3)+sqrt(7))/7)a n d1n((sqrt(3)+sqrt(5))/2) 1n((sqrt(3)+sqrt(7))/2) (c) 1n((sqrt(7)-sqrt(3))/2) +-1n((sqrt(3)+sqrt(7))/2)

The abscissas of point Pa n dQ on the curve y=e^x+e^(-x) such that tangents at Pa n dQ make 60^0 with the x-axis are. )a) 1n((sqrt(3)+sqrt(7))/7)a n d1n((sqrt(3)+sqrt(5))/2) (b) 1n((sqrt(3)+sqrt(7))/2) (c) 1n((sqrt(7)-sqrt(3))/2) (d) +-1n((sqrt(3)+sqrt(7))/2)