Pismeni zadaci

Zadatak 1996

Test: MPsIIVAI_345

 

N Uprosti izraz (\(x\geq 1\)): $$\left (\left ( \sqrt{x}+2\sqrt{\frac{x-1}{x}} \right )^{\frac{1}{2}} + \left ( \sqrt{x} -2\sqrt{\frac{x-1}{x}}\right )^{\frac{1}{2}}  \right )^{\frac{1}{4}}$$

Zadatak 1995

Test: MPsIIVAI_345

 

N Dokaži (\(x>0, x \neq 1\)): $$1+\frac{1+\sqrt{x}}{1+x+\sqrt{x}}:\frac{1}{x\sqrt{x}-1}=x$$

Zadatak 1993

Test: MPsIIVAI_345

 

S Uprosti izraz (\(a\neq 0, a\neq \frac{1}{2}\)): $$\frac{4a^2(2a+1)}{1-2a}\cdot \frac{a^2}{4-4a^{-1}+a^{-2}}\cdot \frac{a^{-6}-64}{4+2a^{-1}+a^{-2}}$$

Zadatak 1994

Test: MPsIIVAI_345

 

S Izračunaj:

a) $$\frac{(a^{-2})^3\cdot (b^{-1})^4:(a^{-7}\cdot (b^{-2})^{-3})}{ab^{-2}}$$

b) $$\sqrt{\frac{3+2\sqrt{2}}{3-2\sqrt{2}}+2+\frac{3-2\sqrt{2}}{3+2\sqrt{2}}}$$

Zadatak 1918

Test: MPsIIVAI_329

 

N Uprosti izraz $$\frac{xy-\sqrt{x^2-1}\cdot \sqrt{y^2-1}}{xy+\sqrt{x^2-1}\cdot \sqrt{y^2-1}}$$ ako je $$x=\frac{1}{2}\left ( a+\frac{1}{a} \right ), y=\frac{1}{2}\left ( b+\frac{1}{b} \right ),0<a\leq 1,0<b\leq 1$$

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