Question
If $a^2+b^2+c^2=20$ and $a+b+c=0$, find $a b+b c+c a$.
✓
Answer
Recall the formula
$(a+b+c)^2=a^2+b^2+c^2+2(a b+b c+c a)$
Given that
$a^2+b^2+c^2=20$
$(a+b+c)=0$
Then we have
$(a+b+c)^2=a^2+b^2+c^2+2(a b+b c+c a)$
$(0)^2=20+2(a b+b c+c a)$
$20+2(a b+b c+c a)=0$
$2(a b+b c+c a)=-20$
$(a b+b c+c a)=-10$
$(a+b+c)^2=a^2+b^2+c^2+2(a b+b c+c a)$
Given that
$a^2+b^2+c^2=20$
$(a+b+c)=0$
Then we have
$(a+b+c)^2=a^2+b^2+c^2+2(a b+b c+c a)$
$(0)^2=20+2(a b+b c+c a)$
$20+2(a b+b c+c a)=0$
$2(a b+b c+c a)=-20$
$(a b+b c+c a)=-10$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Find the value of $k$ for which $(x-1)$ is a factor of $\left(2 x^3+9 x^2+x+k\right)$.
→→
If $\text{p(x)}= \text{x}^2-4\text{x}+3,$ evaluate: $\text{p}(2)-\text{p}(-1)+\text{p}\big(\frac{1}{2}\big).$
→ Examine whether the following number are rational or irrational: $\sqrt{8}+4\sqrt{32}-6\sqrt{2}$
→Factorize the following expressions:
$10 x^4 y-10 x y^4$
→$10 x^4 y-10 x y^4$
Write the following in the expanded form: $\Big(\frac{\text{x}}{\text{y}}+\frac{\text{y}}{\text{z}}+\frac{\text{z}}{\text{x}}\Big)^2$
→Prove that: $\frac{\text{x}^{\text{a}(\text{b}-\text{c})}}{\text{x}^{\text{b}(\text{a}-\text{c})}}\div\Big(\frac{\text{x}^\text{b}}{\text{x}^\text{a}}\Big)^\text{c}=1$
→ Find four rational numbers lying between $\frac{3}{7}$ and $\frac{5}{7}.$
→Factorise:
$x^2-4 x+3$
→$x^2-4 x+3$
The radii of two cones are in the ratio $2 : 1$ and their volumes are equal. What is the ratio of their heights?
→