Question 76

If the square of sum of three positive consecutive natural numbers exceeds the sum of their squares by 292, then what is the largest of the three numbers?

Solution

Le the three positive consecutive natural numbers be $$(x-1),(x),(x+1)$$

According to ques,

=> $$[(x-1)+(x)+(x+1)]^2-[(x-1)^2+(x)^2+(x+1)^2]=292$$

=> $$(3x)^2-[(x^2-2x+1)+(x^2)+(x^2+2x+1)]=292$$

=> $$9x^2-3x^2-2=292$$

=> $$6x^2=292+2=294$$

=> $$x^2=\frac{294}{6}=49$$

=> $$x=\sqrt{49}=7$$

$$\therefore$$ Largest of the three numbers = $$7+1=8$$

=> Ans - (D)

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