Algebra Questions
Algebraic identities help simplify expressions and solve mathematical problems using standard formulas. Practise identities involving squares, products, and sums to improve calculation speed for SSC, CHSL, CGL, and other competitive exams.
14 questions
- Simplify the expression: (√3 + √5)² + (√3 − √5)² + 2(√3 + √5)(√3 − √5)
- Simplify: (2√3 + √2)²
- Rationalize: 1 / (√3 + √2)
- Find the value of √(9 + 4√5) + √(9 − 4√5).
- Simplify: (5 + 2√6)(5 − 2√6)
- Simplify: (√12 + √27) ÷ √3
- If \(a+b=\sqrt{17}\) and \(a-b=\sqrt1\), find \(\frac{a^2+b^2}{ab}\).
- If \(x^2+y^2=58\) and \(x+y=10\), then what is the value of \(xy\)?
- Solve: \(\frac{x}{(x+1)}+\frac1x=3\).
- What is the value of the expression \(\sqrt{(12345)^2+12345+12346}\)?
- Find the value of k such that the quadratic equation \(x^2+kx+16=0\) has real and distinct roots.
- Simplify: \(\frac{1}{\sqrt5-2}+\frac{1}{\sqrt5+2}\)
- Find the value of \(\sqrt{12+\sqrt{12+\sqrt{12+\cdots}}}\).
- If \(x+y+z=0\), and \(x^2+y^2+z^2=32\), then find the value of \(xy+yz+zx\).