Question

Simplify:
1 -0.27 ×0.27× 0.27 -0.73 x 0.73 0.73
a] 0.5913 b] 0.4897 c] 0.5003 d] 0.5213​

Answer 1

We have to find the value of

$1 - 0.27\times 0.27\times 0.27 - 0.73\times 0.73\times 0.73$

Step-by-step explanation:

Now, $1 - 0.27\times 0.27\times 0.27 - 0.73\times 0.73\times 0.73$

$= 1 - 0.27^{3} - 0.73^{3}$

$= 1 - (0.27^{3} + 0.73^{3})$

$= 1 - \{(0.27 + 0.73)^{3}- 3\times 0.27\times 0.73\times (0.27 + 0.73)\}$

$= 1 - \{1^{3} - 0.5913\times 1\}$

$= 1 - (1 - 0.5913)$

$= 1 - 1 + 0.5913$

$= \bold{0.5913}$

Thus the required value is a] $0.5913$

Algebraic identity:

$a^{3}+b^{3}=(a+b)^{3}-3ab(a+b)$

$a^{3}-b^{3}=(a-b)^{3}+3ab(a-b)$

$a^{2}+b^{2}=(a+b)^{2}-2ab$

$a^{2}+b^{2}=(a-b)^{2}+2ab$

$a^{2}-b^{2}=(a+b)(a-b)$

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

1 - 0.27 × 0.27 × 0.27 - 0.73 × 0.73 × 0.73

a] 0.5913

b] 0.4897

c] 0.5003

d] 0.5213

FORMULA TO BE IMPLEMENTED

If a + b + c = 0 then

$\sf{ {a}^{3} + {b}^{3} + {c}^{3} = 3abc }$

EVALUATION

Here the given expression is

1 - 0.27 × 0.27 × 0.27 - 0.73 × 0.73 × 0.73

$\sf{ = 1 - {(0.27)}^{3} - {(0.73)}^{3} }$

$\sf{ = {(1)}^{3} + { ( - 0.27)}^{3} + {( - 0.73)}^{3} }$

Let a = 1 , b = - 0.27 , c = - 0.73

Then

a + b + c = 1 - 0.27 - 0.73 = 0

Since a + b + c = 0

$\implies \sf{ {a}^{3} + {b}^{3} + {c}^{3} = 3abc }$

$\sf{ \implies {(1)}^{3} + {( - 0.27)}^{3} + {( - 0.73)}^{3} = 3 \times ( - 0.27) \times ( - 0.73) }$

$\sf{ \implies {(1)}^{3} + {( - 0.27)}^{3} + {( - 0.73)}^{3} = 0.5913 }$

∴ 1 - 0.27 × 0.27 × 0.27 - 0.73 × 0.73 × 0.73

$\sf{ = 1 - {(0.27)}^{3} - {(0.73)}^{3} }$

$\sf{ = {(1)}^{3} + { ( - 0.27)}^{3} + {( - 0.73)}^{3} }$

$= 0.5913$

FINAL ANSWER

Hence the correct option is a] 0.5913

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