Let a, b, x, y be real numbers such that $a^2 + b^2 = 25, x^2 + y^2 = 169$ , and $ax + by = 65$ . If $k = ay - bx$ , then
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Question

Let a, b, x, y be real numbers such that $$a^2 + b^2 = 25, x^2 + y^2 = 169$$, and $$ax + by = 65$$. If $$k = ay - bx$$, then

Accepted Answer

k = 0. ( a x + b y ) 2 = 65 2 \left(ax+by\right)^2=65^2 ( a x + b y ) 2 = 6 5 2 a 2 x 2 + b 2 y 2 + 2 a b x y = 65 2 a^2x^2\ +\ b^2y^2+\ 2abxy\ =\ 65^2 a 2 x 2 + b 2 y 2 + 2 ab x y = 6 5 2 k = a y − b x k = ay - bx k = a y − b x k 2 = a 2 y 2 + b 2 x 2 − 2 a b x y k^2\ =\ a^2y^2+b^2x^2-2abxy k 2 = a 2 y 2

Let a, b, x, y be real numbers such that a2+b2=25,x2+y2=169a^2 + b^2 = 25, x^2 + y^2 = 169a2+b2=25,x2+y2=169, and ax+by=65ax + by = 65ax+by=65. If k=ay−bxk = ay - bxk=ay−bx, then

Let a, b, x, y be real numbers such that a2+b2=25,x2+y2=169a^2 + b^2 = 25, x^2 + y^2 = 169a2+b2=25,x2+y2=169, and ax+by=65ax + by = 65ax+by=65. If k=ay−bxk = ay - bxk=ay−bx, then

Let a, b, x, y be real numbers such that $a^2 + b^2 = 25, x^2 + y^2 = 169$ , and $ax + by = 65$ . If $k = ay - bx$ , then

Let a, b, x, y be real numbers such that $a^2 + b^2 = 25, x^2 + y^2 = 169$ , and $ax + by = 65$ . If $k = ay - bx$ , then