Algebraic Identities

Q.

Formulae for alpha square plus beta square.

Q. If a = 3+2$\sqrt{2}$, find the value of $a^2+\frac{1}{a^2}$.

Q.

Factorize: $3x^2-x-4$.

Q.

If$x+\frac{1}{x}=5$, find the value of $x^3+\frac{1}{x^3}$.

Q.

Factorize: $4x^2+9y^2+16z^2+12xy-24yz-16xz$.

Q.

Factorise$8a^3-b^3-12a^{2}b+6a{b}^2$

Q.

If $x+\frac{1}{x}=\sqrt{5}$, find the values of $x^2+\frac{1}{x^2}and{x}^4+\frac{1}{x^4}$.

Q.

Factorise $x^2-3x-10=0$

Q.

Use suitable identities to find the following product: (3 – 2x) (3 + 2x)

Q.

$Ifx+\frac{1}{x}=2,then{x}^3+\frac{1}{x^3}=$

1. 64

2. 14

3. 8

4. 2

Q.

$\text{If}{x}^3+\frac{1}{x^3}=110,\text{then}x+\frac{1}{x}=$ ?

Q.

If $(x-1)$ is a factor of $a{x}^3-b{x}^2+cx$, what is the value of $a^3-b^3+c^3$?

1. 2abc

2. -2abc

3. 3abc

4. -3abc

Q.

If $x+\frac{1}{x}=4$, then $x^4+\frac{1}{x^4}=$?

Q.

If $x+\frac{1}{x}=11,$ find the value of $x^2+\frac{1}{x^2}$.

Q.

If $x^2+\frac{1}{x^2}=51$, find the value of $x^3-\frac{1}{x^3}$.

Q.

If a + b + c = 9 and ab + bc + ca = 23, find the value of $a^2+b^2+c^2$.

Q.

If $a^2+b^2+c^2=16$ and ab + bc + ca = 10, find the value of a + b + c.

Q.

If $2x+3y=13andxy=6,$ find the value of $8x^3+27y^3.$

Q.

Factorize the following: $27y^3+125z^3$.

Q.

If $x^2+\frac{1}{x^2}=66,$ find the value of $x-\frac{1}{x}$.

Q.

If $x^2+\frac{1}{x^2}=79$, find the value of $x+\frac{1}{x}$.

Q.

If $9x^2+25y^2=181andxy=-6,findthevalueof3x+5y.$

Q. Question 7
If a, b and c are all non-zero and a + b + c = 0, then prove that $\frac{a^2}{bc}+\frac{b^2}{ac}+\frac{c^2}{ab}=3$.

Q.

If $x-\frac{1}{x}=\frac{1}{2}$, then write the value of $4x^2+\frac{4}{x^2}$.

Q.

Factorise: $a^4-b^4$.

Q.

If a + b + c = 9 and ab + bc + ca = 26, find the value of $a^3+b^3+c^3-3abc$.

Q.

If $x-\frac{1}{x}=5$, find the value of $x^3-\frac{1}{x^3}$.

Q.

If a + b + c = 9, and $a^2+b^2+c^2=35$, find the value of $a^3+b^3+c^3-3abc.$

Q.

If x+y+z=9 and xy+yz+zx = 23, the value of $(x^3+y^3+z^3-3xyz)=?$

(a) 108

(b) 207

(c) 669

(d) 729

Q.

If a + b + c = 0 and $a^2+b^2+c^2=16$, find the value of ab + bc + ca.