Question : If $a^{2}=by+cz$, $b^{2}=cz+ax$, $c^{2}=ax+by$, then the value of $\frac{x}{a+x}+\frac{y}{b+y}+\frac{z}{c+z}$ is:

Option 1: $1$

Option 2: $a+b+c$

Option 3: $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}$

Option 4: $0$

Question : If $ax+by=1$ and $bx+ay=\frac{2ab}{a^{2}+b^{2}}$, then $(x^{2}+y^{2})(a^{2}+b^{2})$ is equal to:

Option 1: 1

Option 2: 2

Option 3: 0.5

Option 4: 0

Question : If the sum of the roots of a quadratic equation is 1 and the product of the roots is –20, find the quadratic equation.

Option 1: $x^{2}–x–20=0$

Option 2: $x^{2}+x+20=0$

Option 3: $x^{2}+x–20=0$

Option 4: $x^{2}–x+20=0$

Question : What is the value of ${a}^3+{b}^3+{c}^3$ if $(a+b+c)=0$?

Option 1: $a^2+b^2+c^2-3abc$

Option 2: $0$

Option 3: $3abc$

Option 4: $a^2+b^2+c^2-ab-bc-ca$

Question : The value of $x$ which satisfies the equation $\frac{x \:+\: a^2 \:+\: 2c^2}{b \:+\: c} + \frac{x \:+\: b^2 \:+\: 2a^2}{c+a} + \frac{x \:+\: c^2 \:+\: 2b^2}{a \:+\: b} = 0$ is:

Option 1: $(a^2+b^2+c^2)$

Option 2: $- (a^2+b^2+c^2)$

Option 3: $(a^2+2b^2+c^2)$

Option 4: $-(a^2+b^2+2c^2)$