Rooty & Rational

Algebra Level 2

Let x = 13 ± n x=13\pm \sqrt{n} be the two roots of the quadratic equation for x x 1 3 ( x + m ) 2 = 7 , \frac{1}{3}(x+m)^2=7, where m m and n n are rational numbers. What is the value of n − m ? n-m?

32 36 34 38

Ajay Dutta by Ajay Dutta , 24, India

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3 solutions

Hello,

as 1/3(x+m)^2 = 7,

(x+m)^2 = 7(3)

(x+m)^2 = 21

x+m = +- (21)^0.5

x = +- (21)^0.5

By comparing, x = 13 + +- (n)^0.5 with x= -m + +- (21)^0.5,

m=-13 , n=21, therefore = n-m= 21 + 13 = 34,

thanks...

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Jovert Albos
Feb 28, 2014

frac{1}{3} (X + m)^{2} = 7 Multiply both sides by 3 (X + m)^{2} = 21 X + M = +/- \sqrt{21} X = -M +/- \sqrt{21} By comparing, we see that n = 21 and that m is -13 21 - (-13) = 34

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Farouk Harb
Feb 28, 2014

\frac{1}{3} (X + m)^{2} = 7 Multiply both sides by 3 (X + m)^{2} = 21 X + M = +/- \sqrt{21} X = -M +/- \sqrt{21} By comparing, we see that n = 21 and that m is -13 21 - (-13) = 34

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