The value of \(\dfrac{(2.3)^3 + (1.5)^3 + (1.2)^3 - 3 \times 2.3 \times 1.5 \times 1.2}{(2.3)^2 + (1.5)^2 + (1.2)^2 - 2.3 \times 1.5 - 1.5 \times 1.2 - 1.2 \times 2.3}\) is equal to:
5
Recall the algebraic identity: \(a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca)\).
The given expression is exactly in this form with \(a = 2.3\), \(b = 1.5\), \(c = 1.2\).
Dividing numerator by denominator cancels \((a^2 + b^2 + c^2 - ab - bc - ca)\), leaving simply \(a + b + c\).
Calculate: \(a + b + c = 2.3 + 1.5 + 1.2 = 5.0\).
Hence, the value of the expression is 5.
Similar Questions
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- If $x^4 + \frac{1}{x^4} = 322$, then $x^3 - \frac{1}{x^3} = ?$
- If $(x + \frac{1}{x}) = 7$, then $(x - \frac{1}{x})$ is equal to:
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$(1 + x)(1 + x^2)(1 + x^4)(1 + x^8)(1 - x)$ - If $a + b + c = 17$, $abc = 168$, and $ab + bc + ca = 94$, then $a^3 + b^3 + c^3 = ?$
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Important Questions from Identities
If \(2x + { {1} \over 3x}= 5, x ≠ 0\) , then what is the value of \(27x^3+{{1} \over 8x^3}\) ?
If x 2 + 4y 2 = 40, xy = 6 and x > 2y then the value of x - 2y is:
- \(\dfrac{(0.73)^3+(0.31)^3}{(0.73)^2-0.73\times0.31+(0.31)^2}\)
- \(\dfrac{(5.17-2.19)^2-(5.17+2.19)^2}{11.3223}\)
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?
