Ifodalarni soddalashtirish mavzusidan test savollari

Ushbu \frac{(x+\sqrt{y})\cdot \sqrt{y-2\cdot \sqrt{y}\cdot x+x^{2}}}{y-x^{2}} ifodani x=2\sqrt{6} va y=23 bo‘lganda hisoblang.

Ifodani m=15 va n=3\sqrt{2} bo‘lganda hisoblang.

\frac{(\sqrt{m}+n)\cdot \sqrt{m-2\cdot \sqrt{m}\cdot n+n^{2}}}{m-n^{2}}

Soddalashtiring:

(\frac{1}{\sqrt{a}+\sqrt{b}}-\frac{\sqrt{a}+\sqrt{b}}{a-b})\cdot \frac{a-2\sqrt{a}\sqrt{b}+b}{2\sqrt{b}}

Soddalashtiring:

(\frac{1}{\sqrt{a+1}+\sqrt{a}}+\frac{1}{\sqrt{a}-\sqrt{a-1}})\cdot (\sqrt{a+1}-\sqrt{a-1})

Soddalashtiring:

(\frac{a\sqrt{a}+b\sqrt{b}}{\sqrt{a}+\sqrt{b}}-\sqrt{ab}):(a-b)+\frac{2\sqrt{b}}{\sqrt{a}+\sqrt{b}}\cdot (\sqrt{a+1}-\sqrt{a-1})

Ifodani soddalashtiring.

(a\ge 0.5). \sqrt{a^{2}}-\sqrt{a^{2}+a+0.25}+\sqrt{a^{2}-a+0.25}

Agar x=0.5(\frac{\sqrt{a}}{\sqrt{b}}-\frac{\sqrt{b}}{\sqrt{a}}), a>0 va b>0 bo‘lsa, \frac{2b\sqrt{1+x^{2}}}{\sqrt{1+x^{2}}-x} ni hisoblang.

Agar x=e va y=\pi bo‘lsa, \frac{\sqrt{x^{2}-2xy+y^{2}}}{\sqrt{x^{2}+2xy+y^{2}}}+\frac{2x}{x+y} ning qiymatini hisoblang.

Soddalashtiring:

(\frac{1}{\sqrt{a}+\sqrt{a+1}}+\frac{1}{\sqrt{a}-\sqrt{a-1}}):(1+\sqrt{\frac{a+1}{a-1}})

Agar a=(2+\sqrt{3})^{-1} va b=(2-\sqrt{3})^{-1} bo‘lsa, (a+1)^{-1}+(b+1)^{-1} ning qiymatini hisoblang.

Soddalashtiring:
\frac{\sqrt{16x^{2}+9-24x}}{16x^{2}-9}

Agar a=\sqrt{2} va b=\sqrt[3]{3} bo‘lsa, \sqrt{a^{2}-2ab+b^{2}}+\sqrt{a^{2}-2ab+b^{2}} ning qiymatini hisoblang.

Soddalashtiring:

\frac{3}{a-\sqrt{a^{2}-3}}+\frac{3}{a+\sqrt{a^{2}-3}}

Agar a=0.0025 bo‘lsa, \frac{\sqrt{(a+2)^{2}-8a}}{\sqrt{a}-\frac{2}{\sqrt{a}}} ifodaning qiymatini hisoblang.

Agar a=4^{-1};b=4^{2a} va c=4^{b} bo‘lsa, \frac{ac}{b} ifodaning qiymati nechaga teng bo‘ladi?

Agar a=\frac{1}{2}(\sqrt{\frac{2}{3}}+\sqrt{\frac{3}{2}}) bo‘lsa, \frac{\sqrt{a^{2}-1}}{a-\sqrt{a^{2}-1}} ning qiymatini toping.

x=5\sqrt{6} va y=6\sqrt{5} bo‘lsa, \sqrt{x^{2}+2xy+y^{2}}-\sqrt{x^{2}-2xy+y^{2}} ning qiymatini hisoblang.

Agar a=5.2 bo‘lsa, \frac{a^{2}-a-6-(a+3)\sqrt{a^{2}-4}}{a^{2}+a-6-(a-3)\sqrt{a^{2}-4}} ning qiymatini toping.

Soddalashtiring.

(\frac{1}{a+\sqrt{2}}-\frac{a^{2}+2}{a^{3}+2\sqrt{2}})^{-1}\cdot (\frac{a}{2}-\frac{1}{\sqrt{2}}+\frac{1}{a})^{-1}\cdot \frac{\sqrt{2}}{a+\sqrt{2}}

Soddalashtiring:

(\frac{1+\sqrt{x}+x}{x\sqrt{x}-1})^{-1}-x^{\frac{1}{2}}

Soddalashtiring:

\frac{\sqrt{x}+1}{x\sqrt{x}+x+\sqrt{x}}:\frac{1}{\sqrt{x}-x^{2}}+x

\frac{3}{a-\sqrt{a^{2}-3}}+\frac{3}{a+\sqrt{a^{2}-3}} ni soddalashtiring.

Soddalashtiring:

(\frac{\sqrt{y}-\sqrt{x}}{y-\sqrt{xy}+x}+\frac{x}{x\sqrt{x}+y\sqrt{y}})\cdot \frac{x\sqrt{x}+y\sqrt{y}}{y^{3}}

Soddalashtiring:

\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}} (1\le x\le 2)

\frac{c-2\sqrt{c}+1}{\sqrt{c}-1} kasrni qisqartiring.

Agar x=\frac{4}{5}m bo‘lsa, \frac{\sqrt{m+x}+\sqrt{m-x}}{\sqrt{m+x}-\sqrt{m-x}} ning qiymatini toping.

Agar x<0 bo‘lsa, \sqrt{x^{2}-12x+36}-\sqrt{x^{2}} ni soddalashtiring.

Soddalashtiring:

a\cdot (\frac{\sqrt{a}+\sqrt{b}}{2b\sqrt{a}})^{-1}+b(\frac{\sqrt{a}+\sqrt{b}}{2a\sqrt{b}})^{-1}

\frac{\sqrt{x+4\sqrt{x-4}}-2}{\sqrt{x-4\sqrt{x-4}}+2} ni soddalashtiring.