Evaluate : ((0.43)^3 + (1.47)^3 + (1.1)^3 - 3 x 0.43 x 1.47 x 1.1)/((0.43)^2 + (1.47)^2 + (1.1)^2 - 0.43 x 1.43 - 0.43 x 1.1 - 1.47 x 1.1)

Question

Evaluate :

\(\frac{(0.43)^3 + (1.47)^3 + (1.1)^3 - 3 \times 0.43 \times 1.47 \times 1.1}{(0.43)^2 + (1.47)^2 + (1.1)^2 - 0.43 \times1.43-0.43\times1.1-1.47\times1.1}\)

(a) 1.90 

(b) 2.87 

(c) 3

(d) 3.47

Answer 1

(c) 3

Reqd. exp. is of type \(\frac{a^3 + b^3 + c^3 -3abc}{a^2 + b^2 + c^2 - ab -bc-ca}\)

You know that (a + b + c)(a² + b² + c² - ab - bc - ca) = a³ + b³ + c³ - 3 abc

⇒ a + b + c = \(\frac{a^3 + b^3 + c^3 -3abc}{a^2 + b^2 + c^2 - ab -bc-ca}\)

∴ Reqd. exp. = 0.43 + 1.47 + 1.1 = 3.