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Algebra Level 2

Find the least positive integral possible value of x x which satisfies the inequality

x 2 + 16 x + 64 > 20. \sqrt{x^2+16x+64} > 20.


The answer is 13.

Kritarth Lohomi by kritarth lohomi , 18, India

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2 solutions

Kritarth Lohomi
Mar 7, 2015

The inner expression can be written as ( x + 8 ) 2 = x + 8 \sqrt{\left (x+8\right) ^2} = x+8

So

x + 8 > 20 x+8 > 20

x > 12 x > 12 ⟹ \implies x min. Integral value = 13 x_{\text{min. Integral value}} = \boxed{13}

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Avhipsha Kar
Mar 6, 2015

(x^2 +16x+64 )root over=((x+8)^2) root over=x+8. The least possible value of x to satisfy x+8> 20 is 13......so x=13

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