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ramesh bairwa

· started a discussion

· 1 Months ago

a (Question: 221475.0 )

solution?

Question:
If a + b + c = 4 \(\sqrt{3}\) and a2 + b2 + c2 = 16, then the ratio a : b : c is - 
Options:
A) 1 : 1 : 1
B) 1 : \(\sqrt{2}\)
C) 1 : 2 : 3 
D) None of these
Solution:
Ans: (a) (a + b + c)2 = a2 + b2 + c2 + 2 (ab + bc + ca)

\(\cfrac{48 - 16}{2}\) = ab + bc + ca

16 = ab + bc + ca

\(\therefore\) a2 + b2 + c2 = ab + bc + ca

or a2 – ab + b2 – bc + c2 – ca = 0

\(\Rightarrow\) a(a – b) + b(b – c) + c(c – a) = 0

\(\Rightarrow\) a – b = 0 or a = b, b – c = 0

\(\Rightarrow\) b = c

\(\therefore\) a = b = c

\(\Rightarrow\) a : b : c = 1 : 1 : 1

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