Question
If $a + b + c = 9$ and $ab + bc + ca = 40$, find $a^2 + b^2 +c^2.$
✓
Answer
Recall the formula $(a + b + c)^2$
$= a^2 + b^2 + c^2 + 2(ab + bc + ca)$
.Given that $(a + b + c) = 9$, $ab + bc + ca = 40,$
Then we have $(a + b + c)^2$
$= a^2 + b^2 + c^2 + 2(ab + bc + ca) (9)^2$
$= a^2 + b^2 + c^2 + 2.(40) a^2 + b^2 + c^2 + 80$
$= 81 a^2 + b^2 + c^2$
$= 81 - 80 a^2 + b^2 + c^2$
$= 1$
$= a^2 + b^2 + c^2 + 2(ab + bc + ca)$
.Given that $(a + b + c) = 9$, $ab + bc + ca = 40,$
Then we have $(a + b + c)^2$
$= a^2 + b^2 + c^2 + 2(ab + bc + ca) (9)^2$
$= a^2 + b^2 + c^2 + 2.(40) a^2 + b^2 + c^2 + 80$
$= 81 a^2 + b^2 + c^2$
$= 81 - 80 a^2 + b^2 + c^2$
$= 1$
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
Factorize the following expressions:
$a^3+8 b^3+64 c^3-24 a b c$
→$a^3+8 b^3+64 c^3-24 a b c$
Find the product.
$(x - 2y + 3)(x^2 + 4y^2 + 2xy + 6y - 3x + 9)$
→$(x - 2y + 3)(x^2 + 4y^2 + 2xy + 6y - 3x + 9)$
In the right angled ∆XYZ, ∠XYZ = 90° and a, b, c are the lengths of the sides as shown in the figure. Write the following ratios.
i. sin x
ii. tan z
iii. cos x
iv. tan x.
If $\frac{a}{b}=\frac{7}{3}$, then find the values of the following ratios : $\frac{a^3-b^3}{b^3}$
→Multiply:$\sqrt{10}$ by $\sqrt{40}$
→Given below is the frequency distribution table regarding the concentration of sulphur dioxide in the air in parts per million of a certain city for 30 days.
Find the probability of the concentration of sulphur dioxide in the interval 0.12 - 0.16 on any of these days.
→|
Concentration of $SO_2$
|
0.00 - 0.04
|
0.04 - 0.08
|
0.08 - 0.12
|
0.12 - 0.16
|
0.16 - 0.20
|
0.20 - 0.24
|
|
No. of days
|
4
|
8
|
9
|
2
|
4
|
3
|
Factorize the following polynomials: $(x-3)(x-4) 2(x-5)-6$
→Write the following symbolic statements in words.
i. $\frac{4}{3} \in Q$
ii. $-2 \notin N$
iii. $P=\{p \mid p$ is an odd number $\}$
→i. $\frac{4}{3} \in Q$
ii. $-2 \notin N$
iii. $P=\{p \mid p$ is an odd number $\}$
Define the following terms:
Plane.
Plane.
Show that 5 + √7 is an irrational number.