Advertisements
Advertisements
Question
If a2 + b2 + c2 = 16 and ab + bc + ca = 10, find the value of a + b + c.
Advertisements
Solution
We know that,
`(a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)`
`=> (a + b + c)^2 = 16 + 2(10)` [`∵ a^2 + b^2 + c^2 = 16` and ab + bc + ca = 10]
`=> (a + b + c)^2 = 16 + 20`
`=> (a + b + c) = sqrt36`
`=> a + b + c = +-6`
APPEARS IN
RELATED QUESTIONS
Write the following cube in expanded form:
(2a – 3b)3
Write the following cube in expanded form:
`[3/2x+1]^3`
If 9x2 + 25y2 = 181 and xy = −6, find the value of 3x + 5y
Simplify the following products:
`(x^3 - 3x^2 - x)(x^2 - 3x + 1)`
Write the expanded form:
`(-3x + y + z)^2`
Simplify: `(a + b + c)^2 - (a - b + c)^2`
If \[x - \frac{1}{x} = 7\], find the value of \[x^3 - \frac{1}{x^3}\].
If \[x^2 + \frac{1}{x^2} = 98\] ,find the value of \[x^3 + \frac{1}{x^3}\]
If 2x+3y = 13 and xy = 6, find the value of 8x3 + 27y3
Find the following product:
\[\left( \frac{3}{x} - \frac{5}{y} \right) \left( \frac{9}{x^2} + \frac{25}{y^2} + \frac{15}{xy} \right)\]
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{x}{7} + \frac{y}{3} \right) \left( \frac{x^2}{49} + \frac{y^2}{9} - \frac{xy}{21} \right)\]
If a + b + c = 9 and ab +bc + ca = 26, find the value of a3 + b3+ c3 − 3abc
If \[x^4 + \frac{1}{x^4} = 194,\] then \[x^3 + \frac{1}{x^3} =\]
The product (a + b) (a − b) (a2 − ab + b2) (a2 + ab + b2) is equal to
Use the direct method to evaluate the following products:
(5a + 16) (3a – 7)
Use the direct method to evaluate :
(x+1) (x−1)
Use the direct method to evaluate :
(ab+x2) (ab−x2)
Use the direct method to evaluate :
(0.5−2a) (0.5+2a)
Evaluate: 203 × 197
If a + b + c = 0, then a3 + b3 + c3 is equal to ______.
