algebra

P and Q are two positive integers such that P² = Q² + 13. The product of the numbers P and Q is

What is the value of $\left(\frac{3^{81}}{27^4}\right)^{1 / 3}$ ?

If, for non-zero real variables x, y, and real parameter a > 1, x: y = (a + 1): (a− 1), then, the ratio (x² - y²): (x² + y²) is

If, for non-zero real variables $x$, $y$, and real parameter $a > 1$, $x : y = (a + 1) : (a - 1)$, then, the ratio $(x^2 - y^2) : (x^2 + y^2)$ is

The price of an item is 10% cheaper in an online store S compared to the price at another online store M. Store S charges Rs.150 for delivery. There are no delivery charges for ord...

Which one of the following numbers is exactly divisible by $\left(11^{13}+1\right) ?$

The three roots of the equation f(x) = 0 are x = {-2, 0, 3}. What are the three values of x for which f (x - 3) = 0?

For what values of k given below is $\frac{(k+2)^2}{k-3}$ an integer?

In a quadratic function, the value of the product of the roots (α, β) is 4. Find the value of $\frac{\alpha^n + \beta^n}{\alpha^{-n} + \beta^{-n}}$

Let x and y be integers satisfying the following equations 2x² + y² = 34 x + 2y = 11 The value of (x + y) is _________.

Let y² - 2y + 1 = x and √x + y = 5. The value of x + √y equals _________ (Give the answer up to three decimal places)

The expression $\frac{(x+y)-|x-y|}{2}$ is equal to

For what values of k given below is $${{{{\left( {k + 2} \right)}^2}} \over {k - 3}}$$ an integer?

Functions F(a, b) and G(a, b) are defined as follows: F(a, b) = (a - b) 2 and G(a, b) = |a - b| , where |x| represents the absolute value of x. What would be the value of G(F(1, 3)...

Let $$x$$ and $$y$$ be integers satisfying the following equations $$$2{x^2} + {y^2} = 34$$$ $$$x + 2y = 11$$$ The value of $$(x+y)$$ is _________.

Let $$\,{y^2} - 2y + 1 = x$$ and $$\,\sqrt x + y = 5.\,\,$$ The value of $$\,x + \sqrt y \,\,$$ equals ________. (Given the answer up to three decimal places)

Roots of the algebraic equation $${x^3} + {x^2} + x + 1 = 0$$ are