`sqrt(x+3)+sqrt(x+15)<6`

Prove that (2sqrt(3)+3)sin x+2sqrt(3)cos x lies between -(2sqrt(3)+sqrt(15)) and (2sqrt(3)+sqrt(15))

sqrt(x)+sqrt(5+x)=15/sqrt(5+x)

sqrt(x)+sqrt(5+x)=15/sqrt(5+x)

the equation is sqrt(x+3-4sqrt(x-1))+sqrt(x+15-8sqrt(x-1))=2 has:

Prove that the following equations has no solutions. (i) sqrt((2x+7))+sqrt((x+4))=0 (ii) sqrt((x-4))=-5 (iii) sqrt((6-x))-sqrt((x-8))=2 (iv) sqrt(-2-x)=root(5)((x-7)) (v) sqrt(x)+sqrt((x+16))=3 (vi) 7sqrt(x)+8sqrt(-x)+15/(x^(3))=98 (vii) sqrt((x-3))-sqrt(x+9)=sqrt((x-1))

Evaluate : sqrt( x^3 sqrt ( x^3 sqrt ( x^3 ) ))

If x=(sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3)) and y=(sqrt(5)-sqrt(3))/(sqrt(5)+sqrt(3)), then (x+y) equals (a) 2(sqrt(5)+sqrt(3))( b) 2sqrt(15)(c)8 (d) 16

If x=8 + 2sqrt(15) , then the value of sqrt(x) + 1/sqrt(x) is: