14.
(i) Given (-12)^3 + (7)^3 + (5)^3.
Let x = -12, y = 7, z = 5.
x + y + z = > -12 + 7 + 5 = 0.
We know that when x + y +z = 0, then x^3 + y^3 + z^3 = 3xyz
So, (-12)^3 + (7) + (5)
= > 3(-12)(7)(5)
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(ii)
Given Equation is 4x^2 + 9y^2 + 16z^2 + 12xy - 24yz - 16xz
= > (2x)^2 + (3y)^2 + (4z)^2 + 2(2x)(3y) - 2(3y)(4z) - 2(2x)(4z)
It is in the form of a^2 + b^2 + c^2 + 2ab - 2bc - 2ca = (a + b - c)^2
Hope this helps!
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Answers & Comments
14.
(i) Given (-12)^3 + (7)^3 + (5)^3.
Let x = -12, y = 7, z = 5.
x + y + z = > -12 + 7 + 5 = 0.
We know that when x + y +z = 0, then x^3 + y^3 + z^3 = 3xyz
So, (-12)^3 + (7) + (5)
= > 3(-12)(7)(5)
-------------------------------------------------------------------------------------------------------
(ii)
Given Equation is 4x^2 + 9y^2 + 16z^2 + 12xy - 24yz - 16xz
= > (2x)^2 + (3y)^2 + (4z)^2 + 2(2x)(3y) - 2(3y)(4z) - 2(2x)(4z)
It is in the form of a^2 + b^2 + c^2 + 2ab - 2bc - 2ca = (a + b - c)^2
Hope this helps!