Q&A If a,b are real numbers such that ab-4a+4b=18, find the minimum value of a^2+b^2 Quadratic function
Q&A If x, y \in Z such that x^2+y^2 =4x^3+y^3 = 8Find the value of 2x+y Calculate algebraic expressions
Q&A If a is a root for the following equationx^2+\sqrt{3}x-2 = 0 Find the value of \dfrac{a^4}{a^8+a^6+2a^4+4a^2+16} Nike function
Q&A If f(x)= \begin{cases} \log_{2}x &(x>0) \\ 2^x &(x\leq 0) \end{cases}find the value of f[f(\frac{1}{9})] Logarithm
Q&A Prove\cos(\dfrac{\pi}{4}-x)\cos(\dfrac{\pi}{4}-y) -\sin(\dfrac{\pi}{4}-x)\sin(\dfrac{\pi}{4}-y) =\sin(x+y) Trigonometry
Q&A Find the value of \dfrac{\sqrt{10+\sqrt{1}}+\sqrt{10+\sqrt{2}}+\cdots+\sqrt{10+\sqrt{99}} }{\sqrt{10-\sqrt{1}}+\sqrt{10-\sqrt{2}}+\cdots+\sqrt{10-\sqrt{99}}} Trigonometry
Q&A Show that \dfrac{\sqrt{1+\sin x}+\sqrt{1+\cos x} }{\sqrt{1-\sin x}+\sqrt{1-\cos x} } =\sqrt{2}+1 Trigonometry
Q&A Given a,b,c are positive real numbers such that a+b+c = \sqrt{10+\sqrt{19} } and\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c} = \sqrt{10-\sqrt{19} } If x = a^2+b^2+c^2, find the value of x+\dfrac{9}{x} Inequality
