`x^(2)-(sqrt(7)+1)x+sqrt(7)=0`

Show that : (1)/(3-2sqrt(2))- (1)/(2sqrt(2)-sqrt(7)) + (1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)-2)=5 .

Solve the following quadratic equations : (i) 9x^(2) - 8x+2=0 (ii) sqrt7 x^(2) +x+ sqrt7=0 (iii) 2sqrt3x^(2) -sqrt2 x + 3sqrt3 =0

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

Prove that (1)/(sqrt(7))=(1)/(sqrt(7))times(sqrt(7))/(sqrt(7))

If 0ltxltpi and cosx + sinx =1/2 , then tanx is (1) (4-sqrt(7))/3 (2) -(4+sqrt(7))/3 ( 3) (1+sqrt(7))/4 (4) (1-sqrt(7))/4

Prove that the following equations has no solutions. (i) sqrt((2x+7))+sqrt((x+4))=0

Rationalise the denominators of the following:(i) 1/(sqrt(7)) (ii) 1/(sqrt(7)-sqrt(6)) (iii) 1/(sqrt(5)+sqrt(2)) (iv) 1/(sqrt(7)-2)

Rationalise the denominators of the following:(i) 1/(sqrt(7)) (ii) 1/(sqrt(7)-sqrt(6)) (iii) 1/(sqrt(5)+sqrt(2)) (iv) 1/(sqrt(7)-2)

Prove that tan [7(1)/(2)]^0 = (sqrt(3) - sqrt(2)) (sqrt(2) - 1) .

Evaluate the following limits : Lim_(x to 0 ) (sqrt(1+x)-sqrt(1+x^(2)))/(sqrt(1-x^(2))-sqrt(1-x))