KVS MATHEMATICS QUIZ 4 (ALGEBRA)

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Question 1:

If $x^{2}+y^{2}+z^{2}=x y+y z+z x$, then value of, $\frac{7 x^{7}+9 y^{5}+11 z^{3}}{4 x^{3} y^{2}+3 y^{3} z^{2}+2 z^{3} x^{2}}$ is:

Question 2:

The value of

$\frac{(2.9)^{3}+(8.7)^{3}}{(2.9)^{2}-2.9 \times 8.7+(8.7)^{2}}$ is:

Question 3:

What is the value of the expression?

$\frac{(a-b)^{3}+(b-c)^{3}+(c-a)^{3}}{3(a-b)(b-c)(c-a)}=\text { ? }$

Question 4:

Which of the following option is correct.

$a^{3}+b^{3}=(a-b)\left(a^{2}+b^{2}+a b\right)$

$a^{3}+b^{3}=(a+b)\left(a^{2}-b^{2}-a b\right)$

$a^{3}-b^{3}=(a-b)\left(a^{2}+b^{2}-a b\right)$

$a^{3}+b^{3}=(a+b)\left(a^{2}+b^{2}-a b\right)$

Question 5:

If $(a+b+c)=0$ and $(a b c)=12$, then what is the value of $\left(a^{3}+b^{3}+c^{3}\right) ?$

Question 6:

If $(3+2 \sqrt{2}) a=(3-2 \sqrt{2}) b$, then $\frac{1}{a}+\frac{1}{b}$ is:

Question 7:

If $a+\frac{1}{a+2}=0$, then the value of $(a+2)^{3}+\frac{1}{(a+2)^{3}}$:

Question 8:

If $a^{2}+b^{2}=40$ and $a b=10$ then the value of $(\sqrt{a-b})^{2}$ is ?

Question 9:

If $x=5-\frac{1}{x}$ then what is value of $x^{2}+\frac{1}{x^{2}}$.

Question 10:

Solve : $a^{2}-b^{2}=?$

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