EXEMPLARY QUESTION TYPES
9.
\(a+\samefrac3{a-2}=9\)
\(\Rightarrow\left(a-2\right)^2+\samefrac9{\left(a-2\right)^2}=?\)
10.
\(x^2-7x+1=0\)
\(\Rightarrow x^2+\samefrac1{x^2}=?\)
11.
\(x^2-5x+2=0\)
\(\Rightarrow x^2+\samefrac{10}x=?\)
12.
\(x^2+x+1=0\)
What is the value of \(x^{92}\) in terms of \(x\)?
13.
\(x\in\mathbb R\)
\(A=x^2-3x+1\)
\(\Rightarrow\min\left(A\right)=?\)
14.
\(a\cdot b\cdot c\in\mathbb R\)
\(a^2+b^2+c^2-2a+4b+6c+14=0\)
\(\Rightarrow a\cdot b\cdot c=?\)
15.
\(\samefrac{a^4-19a^2+9}{a^2-5a+3}=?\)
16.
\(A=\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(\Rightarrow\samefrac{A+1}{2^8}=?\)