Question 111

What is the Value of $$\frac{0.74 \times 1.23 \times 0.13}{(0.37)^3 + (0.41)^3 - 8(0.39)^3}$$?

Solution

Expression : $$\frac{0.74 \times 1.23 \times 0.13}{(0.37)^3 + (0.41)^3 - 8(0.39)^3}$$

= $$\frac{(0.37\times2) \times (0.41\times3) \times 0.13}{(0.37)^3 + (0.41)^3 - (2\times0.39)^3}$$

= $$\frac{0.37 \times 0.41\times 0.78}{(0.37)^3 + (0.41)^3 - (0.78)^3}$$

Let $$x=0.37$$, $$y=0.41$$ and $$z=-0.78$$

$$\because$$ $$x+y+z=0$$, => $$x^3+y^3+z^3=3xyz$$

=> $$\frac{xy(-z)}{x^3+y^3-z^3}=\frac{-1}{3}$$

=> Ans - (A)


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