Question

The value of x^3 + y^3+ z^3 - 2xyz, if
x = root7- root 5, y = root 5- root 3 and z = root 3-root 7 is​

Answer 1

Answer:

Step-by-step explanation:

x=√7-√5, y=√5-√3, z=√3-√7

x³=(√7-√5)³=√7³-3.√7².√5+3.√7.√5²-√5³=7√7-21√5+15√7-5√5=22√7-26√5

y³=(√5-√3)³=√5³-3.√5².√3+3.√5.√3²-√3³=5√5-15√3+9√5-3√3=14√5-18√3

z³=(√3-√7)³=√3³-2.√3².√7+2.√3.√7²-√7³=3√3-6√7+14√3-7√7=17√3-13√7

xyz=(√7-√5)(√5-√3)(√3-√7)

     =(√35-5-√21+√15)(√3-√7)

     =√105-5√3-3√7+3√5-7√5+5√7+7√3-√105

     =2√3+2√7-4√5

∴, x³+y³+z³-2xyz

=22√7-26√5+14√5-18√3+17√3-13√7-2(2√3+2√7-4√5)

=9√7-12√5-√3-4√3-4√7+8√5

=5√7-4√5-5√3

hope it helps u

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