vereinfachen (sqrt(3/5)x+sqrt(3/11)y)^2

Lösung

vereinfachen

(\frac{3}{5} x + \frac{3}{11} y)^{2}

\frac{6 55 x y + 33 x ^{2} + 15 y ^{2}}{55}

Schritte zur Lösung

(\frac{3}{5} x + \frac{3}{11} y)^{2}

Wende Formel für perfekte quadratische Gleichungen an:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(\frac{3}{5} x + \frac{3}{11} y)^{2} = (\frac{3}{5} x)^{2} + 2 \frac{3}{5} x \frac{3}{11} y + (\frac{3}{11} y)^{2}

= (\frac{3}{5} x)^{2} + 2 \frac{3}{5} x \frac{3}{11} y + (\frac{3}{11} y)^{2}

Vereinfache

(\frac{3}{5} x)^{2} + 2 \frac{3}{5} x \frac{3}{11} y + (\frac{3}{11} y)^{2} : \frac{110 \frac{3}{5} \frac{3}{11} x y + 33 x ^{2} + 15 y ^{2}}{55}

= \frac{110 \frac{3}{5} \frac{3}{11} x y + 33 x ^{2} + 15 y ^{2}}{55}

110 \frac{3}{5} \frac{3}{11} x y = 655 x y

= \frac{6 55 x y + 33 x ^{2} + 15 y ^{2}}{55}

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