Question

please solve this maths question

Answer 1

a+b+c=15

a+b+c= 5+5+5

0=(5-a)+(5-b)+(5-c)

Note if x+y+z =0

then x^3 + y^3 + z^3 = 3xyz

Using this we get

(5-a)^3 + (5-b)^3 + (5-c)^3 = 3(5-a)(5-b)(5-c)

so

(5-a)^3 + (5-b)^3 + (5-c)^3 - 3(5-a)(5-b)(5-c) =0

Answer 2

Let

(5-a)=x

(5-b)=y

(5-c) =z .

Since we know that ,

m3+n3+p3 -3mnp =(m+n+p) (m2+ n2+p2-mn-np-mp)

→ (5-a)^3 +(5-b)^3 +(5-c)^3 -3(5-a)(5-b) (5-c) = ( x +y +z) (x2 +y2+z2 -xy -yz - zx)

= (5-a +5-b+5-c) (x2+y2+z2-xy -yz -xz)

=(15-15) (x2+y2+z2-xy -yz -zx)

[since, a+b+c =

15]

=0×(x2+y2+z2-xy -yz -zx)

=0