What-is-the-value-of-a-2-b-2-if-ax-by-3-bx-ay-4-and-x-2-y-2-4-

Question Number 136607 by EDWIN88 last updated on 23/Mar/21

What is the value of a^{2} + b^{2} if ax + by = 3

bx - ay = 4 and x^{2} + y^{2} = 4

Answered by MJS_new last updated on 24/Mar/21

{\begin{cases} a x + b y = 3 \\ b x - a y = 4 \end{cases} \Leftrightarrow {\begin{cases} a = \frac{3 x - 4 y}{x^{2} + y^{2}} \\ b = \frac{4 x + 3 y}{x^{2} + y^{2}} \end{cases} \Rightarrow a^{2} + b^{2} = \frac{25}{x^{2} + y^{2}} = \frac{25}{4}

Answered by mindispower last updated on 24/Mar/21

{(a x + b y)}^{2} + {(b x - a y)}^{2} = (a^{2} + b^{2}) (x^{2} + y^{2}) \dots