If p2 + q2 + 4r2 + 3 = 2p – 2q + 4r, then the value of 2p – 3q + 4

1.	If p2 + q2 + 4r2 + 3 = 2p – 2q + 4r, then the value of 2p – 3q + 4r is (Assume that p, q, r are all real numbers.)
Answer» Correct Answer - Option 4 : 7 Assuming p = 1, q = -1, We get, \(\begin{array}{l} 1 + 1 + 4{r^2} + 3 = 2 - \left( { - 2} \right) + 4r\\ \therefore 4{r^2} - 4r + 1 = 0 \end{array}\) ∴ r = ½ ∴ 2p – 3q + 4r = 2 – (-3) + 2 = 2 + 3 + 2 = 7

If p2 + q2 + 4r2 + 3 = 2p – 2q + 4r, then the value of 2p – 3q + 4r is (Assume that p, q, r are all real numbers.)

Answer» Correct Answer - Option 4 : 7

Assuming p = 1, q = -1,

We get,

\(\begin{array}{l} 1 + 1 + 4{r^2} + 3 = 2 - \left( { - 2} \right) + 4r\\ \therefore 4{r^2} - 4r + 1 = 0 \end{array}\)

∴ r = ½

∴ 2p – 3q + 4r = 2 – (-3) + 2 = 2 + 3 + 2 = 7

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If p2 + q2 + 4r2 + 3 = 2p – 2q + 4r, then the value of 2p – 3q + 4r is (Assume that p, q, r are all real numbers.)

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