Find x - x - b - c - a - x - c - a - b -x- a - b - c -3- if 1- a -1- b -1-e-0A- a-b-cB- None of these C- a b-b c-c aD- a - bc

The correct option is A a + b + c x b c/a+x c a/b+x a b/c=3 It may be written as x b c/a 1+x c a/b 1+x a b/c 1=0 ⇒x b c a/a+x c a b/b+x a b c/c=0 ⇒ (x a b ...

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Quantitative Aptitude

A.M Greater than or Equal to G.M

Find x : x - ...

Question

$Find x : \frac{x - b - c}{a} + \frac{x - c - a}{b} + \frac{x - a - b}{c} = 3, if \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \neq 0$

ab + bc + ca

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a + bc

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a + b + c

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None of these

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Solution

The correct option is C
a + b + c

$\frac{x - b - c}{a} + \frac{x - c - a}{b} + \frac{x - a - b}{c} = 3 It may be written as \frac{x - b - c}{a} - 1 + \frac{x - c - a}{b} - 1 + \frac{x - a - b}{c} - 1 = 0 \Rightarrow \frac{x - b - c - a}{a} + \frac{x - c - a - b}{b} + \frac{x - a - b - c}{c} = 0 \Rightarrow (x - a - b - c) (\frac{1}{a} + \frac{1}{b} + \frac{1}{c}) = 0 S i n c e, \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \neq 0 ∴ x - a - b - c = 0 \Rightarrow x = a + b + c$

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$Find x : \frac{x - b - c}{a} + \frac{x - c - a}{b} + \frac{x - a - b}{c} = 3, if \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \neq 0$

$\frac{x}{a} + \frac{x}{b} + \frac{x}{c} = 1. F i n d t h e v a l u e o f x .$

∣ ∣ ∣ ∣ ∣ \begin{matrix} b^{2} - a b & b - c & b c - a c a b - a^{2} & a - b & b^{2} - a b b c - a c & c - a & a b - a^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣ =

∣ ∣ ∣ ∣ \begin{matrix} a - b - c & 2 a & 2 a 2 b & b - c - a & 2 b 2 c & 2 c & c - a - b \end{matrix} ∣ ∣ ∣ ∣ =

Q. Show that :

∣ ∣ ∣ ∣ ∣ \begin{matrix} b c - a^{2} & c a - b^{2} & a b - c^{2} - b c + c a + c b & b c - c a + a b & b c + c a - a b (a + b) (a + c) & (b + c) (b + a) & (c + a) (c + b) \end{matrix} ∣ ∣ ∣ ∣ ∣ = 3 (b - c) (c - a) (a - b) (a + b + c) (b c + c a + a b)

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Find x : x−b−ca+x−c−ab+x−a−bc=3, if 1a+1b+1c≠0

The correct option is C a + b + c x−b−ca+x−c−ab+x−a−bc=3It may be written asx−b−ca−1+x−c−ab−1+x−a−bc−1=0⇒x−b−c−aa+x−c−a−bb+x−a−b−cc=0⇒(x−a−b−c)(1a+1b+1c)=0Since,1a+1b+1c≠0∴x−a−b−c=0⇒x=a+b+c

$Find x : \frac{x - b - c}{a} + \frac{x - c - a}{b} + \frac{x - a - b}{c} = 3, if \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \neq 0$