If α, β are the roots of 6x²+13x+7=0, then the equation whose roots are α², β² is:

P = 12xy – 10y² – 18x²,

Q = 14x² + 12y² + 9xy, and

R = 5y² – x² + xy

then (P + Q) – R =

If x = 2 then the value of x³ + 27x² + 243x + 631 is

$$ {1\over {^3\sqrt{4}+{^3\sqrt{2}}}+1}=a^3\sqrt{4}+ b^3\sqrt{2}+c $$ and a, b, c are rational numbers, then a + b + c is equal to

When a number x is divided by a divisor it is seen that the divisor = 4 times the quotient=double the remainder. If the remainder is 80 then the value of x is

If (3x – 2y) : (2x + 3y) = 5 : 6, then one of the values of $${\left({^3\sqrt { x}+\ ^3\sqrt { y}\over ^3\sqrt { x}-\ ^3\sqrt { y} } \right) \ }^2$$ is

if $${{5x-7}\over 3}+2={{4x-3}\over 4}+4x$$, then the value of (8x+5) is

$$x+{1\over x}=2$$ and x is real, then the value of $$x^{17}+{1\over x^{19}}$$ is