If `a + b + c = 4 sqrt(3) and a^(2) + b^(2) + c^(2)= 16` then the ratio a : b : c is

Options

A. `1 : 1 : 1`
B. `1 : sqrt2 : sqrt3 `
C. `1: 2: 3`
D. इनमे से कोई नही

Answer

A

Explanation

a + b + e = 4 `sqrt3`
`implies (a + b + c)^2 = 48`
`implies a^2 + b^2 + c^2 + 2ab + 2bc + 2ca = 48`
`implies 16 + 2 (ab + bc + ca) = 48`
`implies 2 (ab + be + ca) = 32`
`implies ab + be + ca = 16`
`implies a = b = c = 4/sqrt3`
`therefore` a : b : c = 1 : 1 : 1