Advertisements
Advertisements
Question
Find: a2 + b2 + c2, if a + b + c = 9 and ab + bc + ca = 24
Sum
Advertisements
Solution
a+ b + c = 9
⇒ (a + b + c)2 = (9)2
⇒ a2 + b2 + c2 + 2ab + 2bc + 2ca = 81
⇒ a2 + b2 + c2 + 2(ab + bc + ca) = 81
⇒ a2 + b2 + c2 + 2×24 = 81
⇒ a2 + b2 + c2 + 48 = 81
⇒ a2 + b2 + c2 = 81 − 48
⇒ a2 + b2 + c2 = 33
shaalaa.com
Application of Formulae
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
If a2 + b2 = 29 and ab = 10, find : a + b
If a2 + b2 = 29 and ab = 10, find : a − b
If a2 + b2= 10 and ab = 3; find : a + b
Find : `"a"^3+1/"a"^3`, if `"a" +1/"a"=5`.
Find:
`a^3-1/a^3`, if `a -1/a = 4`.
If `2"x"-1/(2"x")=4`, find: `8"x"^3-1/(8"x"^3)`
If a2 + b2 = 41 and ab = 4, find : a – b
If a + b + c = 9 and ab + bc + ca = 15, find: a2 + b2 + c2.
If 3x + 2y = 9 and xy = 3, find : 27x3 + 8y3.
If 5x – 4y = 7 and xy = 8, find : 125x3 – 64y3.
