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If x^2 − yz = −5, y^2 − xz = 1 and z^2 − xy = 7, find the value of
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19 Jan 2022, 06:48
19 Jan 2022, 06:48
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If \(x^2 − yz = −5, y^2 − xz = 1\) and \(z^2 − xy = 7,\) find the value of \((x − y)^2 + (y − z)^2 + (z − x)^2.\)
(A) 3
(B) 6
(C) 8
(D) 12
(E) 24
(A) 3
(B) 6
(C) 8
(D) 12
(E) 24
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If x^2 − yz = −5, y^2 − xz = 1 and z^2 − xy = 7, find the value of
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19 Jan 2022, 06:59
19 Jan 2022, 06:59
1
Carcass wrote:
If \(x^2 − yz = −5, y^2 − xz = 1\) and \(z^2 − xy = 7,\) find the value of \((x − y)^2 + (y − z)^2 + (z − x)^2.\)
(A) 3
(B) 6
(C) 8
(D) 12
(E) 24
(A) 3
(B) 6
(C) 8
(D) 12
(E) 24
Take: \((x − y)^2 + (y − z)^2 + (z − x)^2\)
Expand: \((x^2 - 2xy + y^2) + (y^2 - 2yz + z^2) + (z^2 - 2xz + x^2)\)
Simplify: \(2x^2 - 2xy + 2y^2 - 2yz + 2z^2 - 2xz\)
Factor out of the 2 to get: \(2(x^2 - xy + y^2 - yz + z^2 - xz)\)
Rewrite as follows: \(2[(x^2 - yz) + (y^2 - xz) + (z^2 - xy)]\)
Substitute the given values: \(2[(-5) + (1) + (7)]\)
Evaluate: \(2[3] = 6\)
Answer: B
gmatclubot
Re: If x^2 − yz = −5, y^2 − xz = 1 and z^2 − xy = 7, find the value of [#permalink]
19 Jan 2022, 06:59
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