Question

( 16. If 4x2 + y2 = a and xy = b, find the value of 2x+y
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Answer 1

Consider,

$\displaystyle\longrightarrow\sf{4x^2+y^2=a}$

Adding $\displaystyle\sf{4xy=4b}$ to both,

$\displaystyle\longrightarrow\sf{4x^2+4xy+y^2=a+4b}$

$\displaystyle\longrightarrow\sf{(2x)^2+2\cdot2x\cdot y+y^2=a+4b}$

$\displaystyle\longrightarrow\sf{(2x+y)^2=a+4b}$

$\displaystyle\longrightarrow\sf{\underline{\underline{2x+y=\pm\sqrt{a+4b}}}}$