Advertisements
Advertisements
Question
If a + b + c = 9 and ab + bc + ca = 26, find a2 + b2 + c2.
Advertisements
Solution
Given, a + b + c = 9 and ab + bc + ca = 26 ...(i)
Now, a + b + c = 9
On squaring sides, we get
(a + b + c)2 = (9)2
⇒ a2 + b2 + c2 + 2ab + bc + ca = 81 ...[Using identity, (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca]
⇒ a2 + b2 + c2(ab + bc + ca) = 81
⇒ a2 + b2 + c2 + 2(26) = 81 ...[From equation (i)]
⇒ a2 + b2 + c2 = 81 – 52 = 29
APPEARS IN
RELATED QUESTIONS
Factorise:
4x2 + 9y2 + 16z2 + 12xy – 24yz – 16xz
Factorise the following:
27y3 + 125z3
Simplify the following:
322 x 322 - 2 x 322 x 22 + 22 x 22
Write in the expanded form:
`(a + 2b + c)^2`
Write in the expanded form:
(2a - 3b - c)2
Find the value of 27x3 + 8y3, if 3x + 2y = 20 and xy = \[\frac{14}{9}\]
If \[x^4 + \frac{1}{x^4} = 119\] , find the value of \[x^3 - \frac{1}{x^3}\]
Find the following product:
\[\left( 3 + \frac{5}{x} \right) \left( 9 - \frac{15}{x} + \frac{25}{x^2} \right)\]
Find the following product:
Find the following product:
Evaluate:
483 − 303 − 183
If \[x^4 + \frac{1}{x^4} = 623\] then \[x + \frac{1}{x} =\]
The product (x2−1) (x4 + x2 + 1) is equal to
If a2 - 5a - 1 = 0 and a ≠ 0 ; find:
- `a - 1/a`
- `a + 1/a`
- `a^2 - 1/a^2`
Evaluate: (2a + 0.5) (7a − 0.3)
Evaluate, using (a + b)(a - b)= a2 - b2.
999 x 1001
Simplify:
(7a +5b)2 - (7a - 5b)2
Simplify:
`(x - 1/x)(x^2 + 1 + 1/x^2)`
Using suitable identity, evaluate the following:
101 × 102
