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m^2 + n^2 is

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m^2 + n^2 is

by sanju09 » Thu Aug 26, 2010 8:49 pm
If m and n are the roots of the quadratic equation x^2 - (2 √5) x - 2 = 0, the value of m^2 + n^2 is:

A. 32
B. 24
C. 22
D. 20
E. 18


[spoiler]Source: https://gmat-math.blocked/2010/02/4gmat[/spoiler]
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by 4GMAT_Mumbai » Thu Aug 26, 2010 9:07 pm
Hi,

x^2 - (2 √5) x - 2 = 0.

In this quad eqn., sum of roots = 2 root (5) and product of roots = -2

m^2 + n^2 = (m+n)^2 - 2mn

= (2 root 5)^2 - 2(-2)

Hope this helps. Thanks.
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by diebeatsthegmat » Wed Sep 22, 2010 7:42 pm
sanju09 wrote:If m and n are the roots of the quadratic equation x^2 - (2 √5) x - 2 = 0, the value of m^2 + n^2 is:

A. 32
B. 24
C. 22
D. 20
E. 18


[spoiler]Source: https://gmat-math.blocked/2010/02/4gmat[/spoiler]
ehh as what i understood about root, it said x^2- (2 √5) x - 2 = 0 has 2 results x1 and x2 and in this problem its m1 and n
right?
i will solve x^2 - (2 √5) x - 2 = 0 to find m= x1=squrt5-squart7 and m=x2 =sqrt5+squrt7 or m, n respectly
then m^2+n^2=5+7+5+7+2squrt35-2sqrt35=24
the correct answer is B
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