Question

value of (1/3)³+(1/4)³-(7/12)³

Answer 1

Answer:

We know that,

(x+y+z)(x²+y²+z²-xy-yz-zx)=x³+y+z³-3xyz

(x+y+z)(x²+y²+z²-xy-yz-zx)+3xyz-x³+y³+z³ Here x³=(1/4)³, y³-(1/3)³, z³--(7/12)³ Now we have, (1/4)³+(1/3)³-(7/12)³=(1/4+1/3-7/12) (x²+y²+z²-xy-yz-zx)+3(1/4)(1/3)(-7/12)

(1/4)³+(1/3)³-(7/12)³={(3+4-7)/12}(x²+ y²+z²-xy-yz-zx)-21/144

(1/4)³+(1/3)³-(7/12)³={0/12} 3(x²+y²+z²-xy-yz-xz)-21/144

(1/4)³+(1/3)³-(7/12)³=-21/144=-7/48

Hence value of, (1/4)³+(1/3)³-(7/12)³=-7/48

MAY THIS WILL HELP YOU