Given positive even numbers x,y , if x^2y+xy^2=96 , find the value of x^2+y^2

Given positive integers, if x^2+y^2+4y-96=0 , find the value of xy .

If x=2 , y=-\dfrac{1}{2} , find the value of 4x^2y-[6xy-3(4xy-2)-x^2y]+1

Given positive real number m, if m-\cfrac{1}{m}=3 , find the value of m^2-\cfrac{1}{m^2}

(1-\dfrac{1}{2^2} )(1-\dfrac{1}{3^2})(1-\dfrac{1}{4^2}) \dots(1-\dfrac{1}{100^2})

If a+b=0 , find the value of the expression a^3-2b^3+a^2b-2ab^2

If xy=1 , x^2+y^2=2 , find value of x+y

If x^2-3x+1=0 , find the value of x^4+\dfrac{1}{x^4}

If a^{-\frac{1}{2} }= x , where a > 0 and x > 0 , which of the following equations gives a in terms of x ?

If x+y=1 and x^2+y^2=2 , find the value of the algebraic expression x^4+y^4

If n and p are positive and 100n^3p^{-1} = 25n , what is n^{-2} in terms of p ?

For what value of x is the equation 2^{2x + 7}=2^{15} true?