TEST 20
1.
\(\left.\begin{aligned}x^3+6x^2y&=12\\12xy^2+8y^3&=52\end{aligned}\right\}\)
\(\Rightarrow x+2y=?\)
A) \(3\)B) \(4\)C) \(5\)D) \(6\)E) \(8\)
2.
\(\samefrac1a+\samefrac1b+\samefrac1c=\samefrac6{abc}\)
\(a+b+c=5\)
\(\Rightarrow\ a^2+b^2+c^2=?\)
A) \(13\)B) \(12\)C) \(11\)D) \(10\)E) \(9\)
3.
\(x,\ y,\ z\in\mathbb R^+\)
\(x^2+y^2+z^2=16\)
\(xy+yz+xz=10\)
\(\Rightarrow\ x+y+z=?\)
A) \(7\)B) \(6\)C) \(5\)D) \(4\)E) \(3\)
4.
\(x,\ y,\ z\in\mathbb R^+\)
\(\left.\begin{aligned}x^2+2xy&=3\\y^2+2yz&=8\\z^2+2xz&=5\end{aligned}\right\}\)
\(\Rightarrow\ x+y+z=?\)
A) \(2\)B) \(3\)C) \(4\)D) \(5\)E) \(\sqrt{15}\)
5.
\(x,\ y,\ z\in\mathbb R\)
\(\left.\begin{aligned}x^2+y^2+z^2&=10\\xy-yz+xz&=3\end{aligned}\right\}\)
\(\Rightarrow\ \lvert x-y-z\rvert=?\)
A) \(1\)B) \(2\)C) \(3\)D) \(4\)E) \(5\)
6.
\(a-c=7\)
\(c-b=7\)
\(\Rightarrow\ a^2+b^2-2c^2=?\)
A) \(49\)B) \(63\)C) \(91\)D) \(98\)E) \(105\)
7.
\(x-y=1\)
\(\Rightarrow\ \samefrac{x^2-y^2+6y-9}{x^2-y^2-3x+3y}=?\)
A) \(1\)B) \(2\)C) \(3\)D) \(4\)E) \(5\)
8.
\(a,\ b\in\mathbb R\)
\(a\cdot b<0\)
\(6a^2-ab-2b^2=0\)
\(\Rightarrow\ \samefrac ab=?\)
A) \(-1\)B) \(-\samefrac12\)C) \(-\samefrac23\)D) \(\samefrac12\)E) \(\samefrac13\)