Question
Download Solution PDFThe value of \(\frac{4.169\times4.169\times4.169-64\times(0.728)^3}{(4.169)^2+(2.912)^2+8\times(0.364)(4.169)}\) is (2 - k). What is the value of k?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
\(\frac{4.169\times4.169\times4.169-64\times(0.728)^3}{(4.169)^2+(2.912)^2+8\times(0.364)(4.169)}\) = (2 - k)
Concept used:
a3 - b3 = (a - b)(a2 + ab + b2)
Calculation:
\(\frac{4.169\times4.169\times4.169-64\times(0.728)^3}{(4.169)^2+(2.912)^2+8\times(0.364)(4.169)}\) = (2 - k)
⇒ \(\frac{{4.169}^3 -(4 \times 0.728)^3}{(4.169)^2+(2.912)^2+(2.912)(4.169)}\) = (2 - k)
⇒ \(\frac{{4.169}^3 -(2.912)^3}{(4.169)^2+(2.912)^2+(2.912)(4.169)}\) = (2 - k)
⇒ \(\frac{(4.169 - 2.912) \times ((4.169)^2+(2.912)^2+(2.912)(4.169))}{(4.169)^2+(2.912)^2+(2.912)(4.169)}\) = (2 - k)
⇒ (4.169 - 2.912) = (2 - k)
⇒ 1.257 = (2 - k)
⇒ k = 2 - 1.257
⇒ k = 0.743
∴ The value of k is 0.743.
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