Question

find 16y^2+x^2 if 4y+x=7 and xy=3​

Answer 1

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Answer 2

Answer:

The value of the given algebraic expression is $25.$

Step-by-step explanation:

The given equations are:

$4y+x=7......(i)\\xy=3.......(ii).$

Th equation $(ii)$ can be written as: $y=\frac{3}{x}......(iii)$

Now we put the value $y$ in the equation $(i).$

We get,

$4.\frac{3}{x}+x=7\\ = > 12+x^{2} =7x\\= > x^{2} -7x+12=0\\= > x^{2} -4x-3x+12=0\\= > x(x-4)-3(x-4)=0\\= > (x-4)(x-3)=0= > x-4=0 or x-3=0\\= > x=4 or x=3.$

Now put $x=3$ in the equation $(iii).$

We get,

$y=\frac{3}{3}\\ = > y=1.$

Now we put the value of $x,y$ in the expression $16y^{2}+x^2$ and we get,

$16(1)^2+(3)^2\\=16+9\\=25.$

The required answer is: $25.$