Question

If 2x + y = 14 and xy = 6, find the value of
4x rais to the power 2 + y rais the power 2​

Answer 1

Answer:

$4x^2 + y^2 = 172$

Step-by-step explanation:

Given Equation:

2x + y = 14

Squaring both sides of the equation,

$(2x + y)^2 = (14)^2$

Following the identity $(a + b)^2 = a^2 + b^2 + 2ab$,

$(2x)^2 + y^2 + 2(2x)(y) = 196$

$4x^2 + y^2 + 4xy = 196$

Substituting xy = 6 in the above equation,

$4x^2 + y^2 + 4(6) = 196$

$4x^2 + y^2 + 24 = 196\\4x^2 + y^2 = 196 - 24\\4x^2 + y^2 = 172$