Question

If x2 + y2 = 14 and xy=5, find the value of (½x+½y)².

pls help​

Answer 1

Answer:

(½x+½y)²=6

Step-by-step explanation:

x^2 + y^2 = 14, xy=5

(A+B)^2=A^2 +2AB+B^2... (*)

(1/2x+1/2y)^2 =(*)

(1/2x)^2 +2(1/2x)(1/2y)+(1/2y)^2 =

1/4x^2 +1/2xy+1/4y^2=

1/4(x^2 +y^2) +1/2(xy)=

1/4*14+1/2*5=

14/4+5/2=

14/4+10/4=

24/4=6

Answer 2

Answer:

Step-by-step explanation:

Given: x² + y² = 14 and xy = 5

(a + b)²  = a²  + b²  + 2ab

$(\frac{1}{2}x+\frac{1}{2}y)^{2}=(\frac{1}{2}x)^{2}+(\frac{1}{2}y)^{2}+2*\frac{1}{2}x*\frac{1}{2}y\\\\=\frac{1}{4}x^{2}+\frac{1}{4}y^{2}+x*\frac{1}{2}y\\\\=\frac{1}{4}x^{2}+\frac{1}{4}y^{2}+\frac{1}{2}xy\\\\=\frac{1}{4}*(x^{2}+y^{2})+\frac{1}{2}xy\\\\=\frac{1}{4}*14+\frac{1}{2}*5\\\\=\frac{7}{2}+\frac{5}{2}\\\\=\frac{12}{2}\\\\=6$