Question

The value of \(\dfrac{94.3\times94.3+5.7\times5.7-94.3\times5.7}{9.43\times9.43\times9.43+0.57\times0.57\times0.57}\) is equal to:
1. 1000
2. 10
3. 100
4. 10000

Answer 1

Correct Answer - Option 2 : 10

Formula used:

a3 + b3 = (a + b)(a2 - ab + b2)

Calculation:

\(\dfrac{94.3\times94.3+5.7\times5.7-94.3\times5.7}{9.43\times9.43\times9.43+0.57\times0.57\times0.57}\)

⇒ \(\dfrac{9.43\times9.43\times100+0.57\times0.57\times100-9.43\times0.57\times100}{9.43\times9.43\times9.43+0.57\times0.57\times0.57}\) 

⇒ \(\dfrac{[(94.3)^2+(5.7)^2-94.3\times5.7]\times100}{(9.43)^3+(0.57)^3}\)

⇒ \(\dfrac{[(9.43)^2+(0.57)^2-9.43\times0.57]\times100}{(9.43+0.57){[(9.43)^2+(0.57)^2-9.43\times0.57}]}\)

⇒ \(\dfrac{100}{(9.43+0.57)}\)

⇒ \(\dfrac{100}{10}\)

⇒ 10

∴ The value of \(\dfrac{94.3\times94.3+5.7\times5.7-94.3\times5.7}{9.43\times9.43\times9.43+0.57\times0.57\times0.57}\) is 10