Question

If 4x2 + y2 = a and xy = b, find the value of
2x + y.​

Answer 1

Given ,

4x² + y² = a..(1)

xy = b..(2)

Now, We know that :(2x + y)² = (2x)² + y² + 2 × 2x × y(2x + y)²

= 4x² + y² + 4xy(2x + y)²

= a + 4b.. [ From (1) & (2) ]2x + y

= ± √(a + 4b)

Hence,

The value of 2x + y is ±√(a + 4b)

Hope it will helps ✌

$...$

Answer 2

$\large \clubs \: \: \: \: { \underline{ \sf{ \color{purple}{Question: }}}}$

${ \sf{If \: 4 {x}^{2} + {y}^{2} = \: a \: and \: xy = b, \: find \: the \: value \: of \:2x + y.}}$

$\large \clubs \: \: \: \: { \underline{ \sf{ \color{purple}{Answer : }}}}$

$\implies { \sf{2x + y = \sqrt{a + 4b}}}$

$\large \clubs \: \: \: \: { \underline{ \sf{ \color{purple}{Solution : }}}}$

$\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Given : - }}}}}$

Here It is given that ,

$\longmapsto \sf{4x² + y² = a \: \: \: \qquad{eqation (1)}}$

$\longmapsto \sf{xy = b \: \: \: \qquad{eqation \: (2)}}$

$\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{( 2x + y )² = ( 2x )² + (y)² + 2 × 2x × y}}}}}$

we may write the above equation by using equation (1) & equation (2),

$\longmapsto \sf{( 2x + y )² = 4x² + y² + 4xy}$

$\longmapsto{\sf{( 2x + y )² = a + 4b}}$

• ➣ from Equation 1 and 2

$\dag \: \: { \underline{ \boxed { \color{red}{\sf{So, \: 2x + y = ± √( a + 4b )}}}}}$