Title: Irratsionaalse algebralise murru taandamine/ÜLESANDED (2)

Ilma pealkirjata Question Set

Credits: licence CC BY-SA 4.0

Irratsionaalse algebralise murru taandamine

Test 2

Taanda murd. Leia puuduvad suurused.

Q: $$\dfrac{7-2\sqrt{7x}+x}{\sqrt{7x}-x}=\dfrac{\sqrt{A}-\sqrt{B}}{\sqrt{C}}$$

$$A=$$[...]

$$B=$$[...]

$$C=$$[...]
A: 7; x; x

Taanda murd. Leia $$K$$ ja $$S$$.

Q: $$\dfrac{\sqrt{mn}+3m}{9m+n+6\sqrt{mn}}=\dfrac{\sqrt{S}}{\left(K \sqrt{m}+\sqrt{n}\right)}$$

$$K=$$[...]

$$S=$$[...]
A: 3; m

Taanda murd. Leia puuduvad suurused.

Q: $$\dfrac{3z^2+6z\sqrt{7}+21}{z\sqrt{7}+7}=\dfrac{M+N\sqrt{7}}{\sqrt{K}}$$

$$M=$$[...], $$N=$$[...], $$K=$$[...]
A: 3z; 3; 7

Taanda murd $$\dfrac{a-\sqrt{a}-2\sqrt{ac}+2\sqrt{c}}{a-\sqrt{a}}$$.

Q: Taanda murd $$\dfrac{a-\sqrt{a}-2\sqrt{ac}+2\sqrt{c}}{a-\sqrt{a}}$$.
- $$\dfrac{\sqrt{a}-2\sqrt{c}}{\sqrt{a}}$$ (correct)
- $$\dfrac{2\sqrt{a}-\sqrt{c}}{\sqrt{a}}$$
- $$\dfrac{\sqrt{a}-\sqrt{c}}{2\sqrt{a}}$$
- $$\dfrac{\sqrt{a}-\sqrt{2c}}{\sqrt{a}}$$

Taanda murd. Leia $$A$$, $$B$$, $$C$$.

Q: $$\dfrac{z-p}{4\sqrt{p}+4\sqrt{z}}=\dfrac{\sqrt{A}-\sqrt{B}}{C}$$

$$A=$$[...]

$$B=$$[...]

$$C=$$[...]
A: z; p; 4

Taanda murd. Leia puuduvad suurused.

Q: $$\dfrac{3\sqrt{3}-2\sqrt{2}}{3\sqrt{3}+2\sqrt{2}}=\dfrac{A-B\sqrt{6}}{C}$$

$$A=$$[...], $$B=$$[...], $$C=$$[...]

Vihje: kasuta kuupide summa ja kuupide vahe valemeid. Meenuta, et

$$a\sqrt{a}=\left(\sqrt{a}\right)^3$$.
A: 35; 12; 19