What is the value of \(\frac{{{{\left( {1.2} \right)}^3} + {{\left( {0.8} \right)}^3} + {{\left( {0.7} \right)}^3} - 2.016}}{{\left( {1.35} \right)\left[ {{{\left( {1.2} \right)}^2} + {{\left( {0.8} \right)}^2} + {{\left( {0.7} \right)}^2} - 0.96 - 0.84 - 0.56} \right]}}?\)
2
Let \(a=1.2,\ b=0.8,\ c=0.7\). Then \(3abc=2.016\) and \(ab+bc+ca=0.96+0.56+0.84\), so the bracket equals \(a^2+b^2+c^2-ab-bc-ca\).
Apply the identity:
\[a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)\]
The bracket cancels, leaving \(\dfrac{a+b+c}{1.35}=\dfrac{2.7}{1.35}=\mathbf{2}\).
Similar Questions
Simplify (x - y + z) 2- (x - y - z) 2.
If 27x 3 – 64y 3 = (Ax + By) (Cx 2 – Dy 2 + 12xy), then the value of 4A + B + 3C + 2D is:
If abc = 5, what is the value of (\({1 \over 1 \ + \ a \ + \ b^{-1} }\) + \({1 \over 1 \ + \ b \ + \ 5 c^{-1}}\) +\(\frac{1}{1+\frac{c}{5}+a^{-1}}\) \(\) )?
If 4(z + 7) (2z – 1) = Az2 + Bz + C, then the value of A + B + C is:
If 2x 2 - 7x + 5 = 0, then what is the value of \(x^3+\frac{125}{8x^3}\) ?
If x 2+ 3x + 1 = 0, then what is the value of \({x^6}\; + \;\frac{1}{{{x^6}}}?\)
Simplify the following expression.
\(\frac{(375+125)^2-(125-375)^2}{375\times375-125\times125}\)
If (16√2x 3+ 81√3y 3) ÷ (2√2x + 3√3y) = Ax 2+ By 2+ Cxy, then find the value of 2A - 3B - 2√6C.
The value of \(\frac{(2.53)^3+(2.47)^3}{25.3×25.3-624.91+24.7×24.7} \) is 5 × 10 k where the value of k is:
If x + y = 12 and xy = 27, x > y, then the value of (x 3– y 3) is:
Important Questions from Identities
If x 2 + 4y 2 = 40, xy = 6 and x > 2y then the value of x - 2y is:
- \(\dfrac{(5.17-2.19)^2-(5.17+2.19)^2}{11.3223}\)
If a(a + b + c) 2= 1792; b(a + b + c) 2= 1536; c(a + b + c) 2= 768 then what will be the value of a?
If a + b + c = 5, a 2+ b 2+ c 2= 27, a 3 + b 3 + c 3 = 125, then the value of \(\frac{abc}{5}\) is:
(999) 2- 2 2=
