3 years ago

If x^2+y^2=14 annd xy=5 find the value of (1/2x+1/2y)^2

Mathematics

1 answer:

Leviafan [203]3 years ago

4 0

Answer:

Step-by-step explanation:

$\left(\frac12x+\frac12y\right)^2=\\\\=\left[\frac12(x+y)\right]^2=\\\\=\left(\frac12\right)^2\left(x+y\right)^2=\\\\=\frac14\left(x+y\right)^2=\\\\=\frac14(x^2+2xy+y^2)=\\\\=\frac14(x^2+y^2+2xy)=\\\\=\frac14(14+2\cdot5)=\\\\=\frac14\cdot28=\\\\=7$

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