Find the value of x3-y3-z3-2xyz- if x-7-5- y-5-3-z-3-7

The correct option is D 2√(7)+2√(3) 4√(5) as x+y+z=0 x^3+y^3+z^3=3xyz so x^3+y^3+z^3 2xyz=xyz=(√(7) √(5))(√(5) √(3))(√(3) √(7))=2√(7)+2√(3) ...

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A.M Greater than or Equal to G.M

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Find the value of $x^{3} + y^{3} + z^{3} - 2 x y z$ , if $x = \sqrt{7} - \sqrt{5}, y = \sqrt{5} - \sqrt{3}, z = \sqrt{3} - \sqrt{7}$

2 \sqrt{7} - 2 \sqrt{3} + 4 \sqrt{5}

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2 \sqrt{7} + 2 \sqrt{3} + 4 \sqrt{5}

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2 \sqrt{7} - 2 \sqrt{3} - 4 \sqrt{5}

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2 \sqrt{7} + 2 \sqrt{3} - 4 \sqrt{5}

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Solution

The correct option is D $2 \sqrt{7} + 2 \sqrt{3} - 4 \sqrt{5}$
as x+y+z=0
$x^{3} + y^{3} + z^{3} = 3 x y z$
so $x^{3} + y^{3} + z^{3} - 2 x y z = x y z = (\sqrt{7} - \sqrt{5}) (\sqrt{5} - \sqrt{3}) (\sqrt{3} - \sqrt{7}) = 2 \sqrt{7} + 2 \sqrt{3} - 4 \sqrt{5}$

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then the value of

x^{3} + y^{3} + z^{3} - 2 x y z

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Find the value of x3+y3+z3−2xyz, if x=√7−√5,y=√5−√3,z=√3−√7

The correct option is D 2√7+2√3−4√5as x+y+z=0x3+y3+z3=3xyzso x3+y3+z3−2xyz=xyz=(√7−√5)(√5−√3)(√3−√7)=2√7+2√3−4√5

Find the value of $x^{3} + y^{3} + z^{3} - 2 x y z$ , if $x = \sqrt{7} - \sqrt{5}, y = \sqrt{5} - \sqrt{3}, z = \sqrt{3} - \sqrt{7}$

The correct option is D $2 \sqrt{7} + 2 \sqrt{3} - 4 \sqrt{5}$
as x+y+z=0
$x^{3} + y^{3} + z^{3} = 3 x y z$
so $x^{3} + y^{3} + z^{3} - 2 x y z = x y z = (\sqrt{7} - \sqrt{5}) (\sqrt{5} - \sqrt{3}) (\sqrt{3} - \sqrt{7}) = 2 \sqrt{7} + 2 \sqrt{3} - 4 \sqrt{5}$