SSC CGL MOST PROBABLE - ALGEBRA QUIZ- 18

If $a+b+c=12$ and $a^2+b^2+c^2=134$ then find the value of $bc(b+c)+ac(c+a)+ab(a+b)+3abc$

If $\frac{4}{1+\sqrt{2}+\sqrt{3}}=a+b\sqrt{2}-c\sqrt{3}-d\sqrt{6}$, where $a,b,c,d$ are natural numbers, then the value of $a+b+c+d$ is?

If $3^a={27}^b={81}^c$ and $abc=144$, then find the value of $36(\frac{1}{a}+\frac{1}{2b}+\frac{1}{5c})$ is?

If the value of $(a+b-2{)}^2+(b+c-5{)}^2+(c+a-5{)}^2=$ then the value of $\sqrt{(b+c{)}^a+(c+a{)}^b}$ is?

If $b+c=ax,c+a=by,a+b=cz$, then the value of $\frac{1}{18}[\frac{1}{x+1}+\frac{1}{y+1}+\frac{1}{z+1}]$ is?

If $27(x+y{)}^3-8(x-y{)}^3=(x+5y)(A{x}^2+B{y}^2+Cxy)$ then what is the value of $(A-B-C)$?

If $a+b+c=11,ab+bc+ca=3$ and a b c =-135, then what is the value of $a^3+b^3+c^3?$

On simplification, $\frac{x^3-y^3}{x[(x+y{)}^2-3xy]}$ $÷\frac{y[(x-y{)}^2+3xy]}{x^3+y^3}\times \frac{(x+y{)}^2-(x-y{)}^2}{x^2-y^2}$ is equal to:

If $a=\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$ and $b=\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$ then $\frac{a^2}{b}+\frac{b^2}{a}$

If $x^4+x^2{y}^2+y^4=28$ and $x^2+xy+y^2=7$, then the value of $(\frac{1}{x^2}+\frac{1}{y^2})$.