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merrygraceapita @merrygraceapita

August 2022 1 14 Report

2. What is the possible largest value of k such that (16x2 + kx - 13x + 49) is a perfect square?

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EngrJohann

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$\Large \mathbb{SOLUTION:}$

$\begin{array}{l} \small \tt 16x^2 + kx - 13x + 49 = 16x^2 + (k - 13)x + 49 \\ \\ \qquad \tt a = 16\: \big | \: b = k - 13\: \big | \: c = 49 \\ \\ \textsf{Note that if the discriminant }\tt b^2 - 4ac\textsf{ is equal} \\ \textsf{to }\tt 0,\textsf{the quadratic equation has }\tt 1\textsf{ real solution} \\ \textsf{which means that the equation is a perfect} \\ \textsf{square.} \\ \\ \textsf{Solving for }\tt k, \\ \\ \tt b^2 - 4ac = 0 \\ \\ \tt (k - 13)^2 - 4(16)(49) = 0 \\ \\ \tt (k - 13)^2 = 4(16)(49) \\ \\ \tt \sqrt{(k - 13)^2} = \sqrt{4(16)49)} \\ \\ \tt k - 13 = \pm\ 2(4)(7) \\ \\ \tt k = 13 \pm 56 \\ \\ \tt k = \{-43, 69\} \\ \\ \therefore \boxed{\textsf{The possible largest value of }\tt k\textsf{ is }\tt 69.} \end{array}$

merrygraceapita d ko tlga maintindihan

EngrJohann Inaayos ko pa

merrygraceapita thankyou..

EngrJohann You're welcome!

iamstup1dplsh3lp HELLO PO!!~ pwede po bang pasagot po ng question ko po dun po sa profile ko po?? thankyou po!! :D

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