Ikkinchi va undan yuqori darajali tenglamalar sistemasi mavzusidan test savollari

Agar m^{2}-mn=48 va n^{2}-mn=52 bo‘lsa, m-n nechaga teng?

Agar \begin{cases}x^{2}-2xy+y^{2}=9 \\ xy=10 \end{cases} bo‘lsa, |x+y| ni hisoblang.

Agar xy=6, yz=2 va xz=3 (x>0) bo‘lsa, xyz ni toping.

Agar x^{2}+y^{2}=225 va x^{2}-y^{2}=63 bo‘lsa, \vert x\vert -|y| ni toping.

Agar p^{2}+pq=96 va q^{2}+pq=48 bo‘lsa, p+q ning qiymati qanchaga teng bo‘ladi?

Tenglamalar sistemasini yeching.

\begin{cases}x^{2}-1=0 \\ xy^{2}=-4 \end{cases}

(x+y)^{2} ni toping.

\begin{cases}x^{2}+y^{2}=10\\xy=3\end{cases}

Agar xy=4, yz=7 va xz=28 (y>0) bo‘lsa, xyz ni toping.

Tenglamalar sistemasini yeching.

\begin{cases}y-x^{3}=0 \\ y=16x \end{cases}

Agar ab=18, bc=25 va ac=8 bo‘lsa, \sqrt{abc} nimaga teng.

Agar a^{2}+b^{2}+ab=91 va a^{2}+b^{2}=61 bo‘lsa, \vert a+b\vert ning qiymati qanchaga teng bo‘ladi?

Agar x^{2}\cdot y=50, x\cdot y^{2}=20 bo‘lsa, xy ning qiymatini hisoblang.

Agar a-b=1 va (a^{2}-b^{2})\cdot (a-b)=9 bo‘lsa, ab ning qiymatini toping.

Agar \begin{cases}x^{2}-5xy+y^{2}=-47 \\ xy=21 \end{cases} bo‘lsa, \vert x+y\vert +|x-y| ning qiymatini toping.

Agar x^{2}-xy=28 va y^{2}-xy=-12 bo‘lsa, |x-y| ning qiymatini aniqlang.

Agar (x-4)^{2}+(x-y^{2})^{2}=0 bo‘lsa, x+2y nechaga teng?

Nechta butun x va y sonlar jufti x^{2}-y^{2}=31 tenglikni qanoatlantiradi?

Agar m va n natural sonlar \sqrt{2}(n-5)+n^{2}-6mn+5m=0 tenglikni qanoatlantirsa, n-m ni toping.

Agar x^{2}\cdot y+x\cdot y^{2}=48 va x^{2}\cdot y-x\cdot y^{2}=16 bo‘lsa, \frac{x}{y} ning qiymatini hisoblang.

Agar \begin{cases}x^{3}+2x^{2}y+xy^{2}-x-y=2 \\ y^{3}+2xy^{2}+x^{2}y+x+y=6 \end{cases} bo‘lsa, x+y ning qiymatini toping.

\begin{cases}x^{3}+y^{3}=35 \\ x+y=5 \end{cases} bo‘lsa, x\cdot y=?

Agar 8a^{3}-b^{3}=37 va ab^{2}-2a^{2}b=-6 bo‘lsa, 2a-b ning qiymatini toping.

a=\frac{25}{a}-b va b=\frac{144}{b}-a bo‘lsa, |a+b| ni hisoblang.

\begin{cases}xy+x+y=11 \\x^{2}y+y^{2}x=30 \end{cases} tenglamalar sistemasi uchun x+y ning katta qiymatini toping.

\begin{cases}y=\frac{4}{x} \\ y=-x^{2}+6x-5 \end{cases} tenglamalar sistemasi nechta yechimga ega?

Agar \begin{cases}\frac{7}{\sqrt{x-7}}-\frac{4}{\sqrt{y+6}}=\frac{5}{3} \frac{5}{\sqrt{x-7}}+\frac{3}{\sqrt{y+6}}=\frac{13}{6} \end{cases} bo‘lsa, x+y ning qiymatini toping.

x ning \begin{cases}x^{5}\cdot y^{7}=32 \\ x^{7}\cdot y^{5}=128 \end{cases} tenglamalar sistemasining yechimidan iborat barcha qiymatlari yig‘indisini toping.

Agar \frac{1}{n}+\frac{1}{m}=\frac{1}{7} va m+n=-4 bo‘lsa, mn ning qiymatini toping.

Agar x^{3}+3xy^{2}=185 va y^{3}+3x^{2}y=158 bo‘lsa, x-y ning qiymatini toping.

Agar \begin{cases}x^{2}y+xy^{2}=120 \\ x^{2}y-xy^{2}=30 \end{cases} bo‘lsa, x^{2}-y^{2} ning qiymatini hisoblang.