Algebra

If 2b = a + c
then show that
(a - b)^2 + 2b^2 + (b - c)^2 = a^2 + c^2

Factorization

Resolve into factors:

Algebra

logarithm

Logarithm

Algebra

If xy = 3(x - 3) and yz = 3(y - 3), show that xz = 3(z -3)                   (Hall)

square root

Find the square root of 3x - 1 + 2√(2x² – 3x - 2)

Square root

Find the square root of 12a + 2b - 4√(6ab)         (Hall)

square root

Find the square root of 2m + 2√(m² – 9n² )      (Hall)

square root

Find the square root of 9m + 8n + 12√(2mn)

Square root

find the square root of √175 - √147

square root

Find the square root of  √32 - √24   (Hall)

square root

Find the square root of 4 +2√3   (Hall)

square root

Find the square root of 10 + 2√24            (Hall)

square root

Find the square root of 38 - 12√10      (Hall)

polynomial

If p, q, r are positive quantities, and the equation

If x⁴ +px³ + qx²+rx + 1 = 0, and

x⁴ +rx³ + qx²+px + 1 = 0, have a common root, then prove that

p + r = q + 2

remainder theorem

If x³ + px + r and 3x² + p have a common factor, 

then p³/27 + r²/4 = 0

Algebra

Algebra

if x + 1/y = 1 and y + 1/z = 1, then show that the value of z + 1/x  = 1

Factorization

Show that: 

ab(x² + 1) – x (a² + b²) = (ax – b) (bx – a)