If `x,a,b` are real prove that `4(a-x)(x-a+sqrt(a^2+b^2))cancelgta^2+b^2`

If x is real,then the maximum value of y=2(a-x)(x+sqrt(x^(2)+b^(2)))

If y=sin^(-1)((a+b cos x)/(b+a cos x)), prove that (dy)/(dx)=-(sqrt(b^(2)-a^(2)))/(b+a cos x)

If x =1/2 (sqrt(a/b)-sqrt(b/a)) then prove that (2asqrt(1+x^2))/(x+sqrt(1+x^2))= a +b

If the roots of the equation x^(2)+2cx+ab=0 are real unequal,prove that the equation x^(2)-2(a+b)x+a^(2)+b^(2)+2c^(2)=0 has no real roots.

If a+b+c=0(a,b, c are real), then prove that equation (b-x)^2-4(a-x)(c-x)=0 has real roots and the roots will not be equal unless a=b=c .

If a^(2) +b^(2) = x, ab = y then the value of (a^(4) +b^(4))/(a^(2) -ab sqrt(2) +b^(2)) is

If x, a, b, c are real and (x-a+b)^(2)+(x-b+c)^(2)=0 , then a, b, c are in

If sinx + siny =a and cos x +cos y =b , show that sin(x+y) = 2ab/(a^(2)+b^(2)) and tan (x-y)/2 = sqrt((4-a^(2) -b^(2))/(a^(2) +b^(2))

If a,b,c,x are all real numbers,and (a^(2)+b^(2))x^(2)-2b(a+c)x+(b^(2)+c^(2))=0 prove that a,b,c are in G.P.,and x is their common ratio.