If x = 8 + 5 x = 8 + \sqrt{5} x = 8 + 5 ​ and y = 8 − 5 y = 8 - \sqrt{5} y = 8 − 5 ​ , then find the value of x 2 + y 2 x^2 + y^2 x 2 + y 2 .

Find the value of *Y* from the system of equations: $$\begin{cases} X - 2Y + 2Z = 16 \\ X - Y + Z =...

Simplify the expression $$\frac{a^{7} \times b^{8} \times c^{7}}{a^{9} \times b^{5} \times c^{4}}$$....

Simplify the expression $$(5z - 12y)^2 + (12z + 5y)^2 - 144z^2$$...

If $x = 4 + \sqrt{6}$ and $y = 4 - \sqrt{6}$, then find the value of $x^2 + y^2$....

Simplify the expression: $$(5z - 7y)^2 + (7z + 5y)^2 - 49z^2$$...

Simplify the expression: $$\frac{a^5 \times b^3 \times c^7}{a^4 \times b^8 \times c^9}$$...