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Algebraic Identity Evaluation

CMAT 2025 · Quantitative Techniques & Data Interpretation · Easy · Quantitative Aptitude

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If x2=y+zx^2 = y + z, y2=z+xy^2 = z + x and z2=x+yz^2 = x + y, then the value of 1x+1+1y+1+1z+1\frac{1}{x+1} + \frac{1}{y+1} + \frac{1}{z+1} is

  1. A.

    -1

  2. B.

    1

  3. C.

    2

  4. D.

    4

Answer

B

Explanation

Given x2=y+zx^2 = y + z. Add xx on both sides: x2+x=x+y+z  ⟹  x(x+1)=x+y+z  ⟹  1x+1=xx+y+zx^2 + x = x + y + z \implies x(x+1) = x + y + z \implies \frac{1}{x+1} = \frac{x}{x+y+z}

Similarly: 1y+1=yx+y+z,1z+1=zx+y+z\frac{1}{y+1} = \frac{y}{x+y+z}, \quad \frac{1}{z+1} = \frac{z}{x+y+z}

Adding these three terms: 1x+1+1y+1+1z+1=x+y+zx+y+z=1\frac{1}{x+1} + \frac{1}{y+1} + \frac{1}{z+1} = \frac{x+y+z}{x+y+z} = 1

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