Q&A If \cosα+\cosβ+\cosγ=0 and \sinα+\sinβ+\sinγ=0, find the value of \cos(α-β) + \cos(β-γ) + \cos(γ - α) Trigonometry

Q&A If x^2+xy+y^2=39, y^2+yz+z^2=49, z^2+zx+x^2=19, find all soltion sets for of x, y , z System of equations

Q&A Show that \sin^2\dfrac{\pi}{14}+\sin^2\dfrac{3\pi}{14}+\sin^2\dfrac{5\pi}{14}=\dfrac{4}{5} Trigonometry

Q&A Find exact value of \sin\dfrac{\pi}{7} \sin\dfrac{2\pi}{7} \sin\dfrac{3\pi}{7} or sin(pi/7)sin(2pi/7)sin(3pi/7) Trigonometry

Q&A If x_1 and x_2 are the two roots of the quadratic equation x^2-px+q=0, (x_1>x_2). Find the values of the following expressions. Algebraic equation

Q&A Let m and n be the two roots of the equation x^2 − 15x + 28 = 0. Find the value of (m + 1)(n + 1) Algebraic equation

Q&A Let x_1 and x_2 be the roots of the equation x^2 + 3x + 1 = 0. Compute\Big( \dfrac{x_1}{x_2+1} \Big) ^2+\Big( \dfrac{x_2}{x_1+1} \Big) ^2 Algebraic equation

Q&A Let x_1 and x_2 be the roots of the equation x^2 − (a + d)x + (ad − bc) = 0. Show that x^3_1 and x^3_2 are the roots of the equationy^2 − (a^3 + d^3 + 3abc + 3bcd)y + (ad − bc)^3 = 0 Algebraic equation

Q&A The depressed cubic equation x^3 +px + 28=0 has three distinct roots. Two of these roots sum to 2. Find the the value of p. Algebraic equation

Multiple choice What is the value of the radical expression\sqrt{6+2\sqrt{2}+2\sqrt{3}+2\sqrt{6} }-\dfrac{1}{\sqrt{5-2\sqrt{6}} } Simplify Radical Expressions

Q&A Show that \sqrt{n-\sqrt{n-\sqrt{n-\sqrt{n-\cdots \infty } } } } = \dfrac{\sqrt{1+4n} -1 }{2} Square Root