Question

In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.

I. \(3{x^2} - 22x + 7 = 0\)

II. \({y^2} - 20y + 91 = 0\)

1. x > y
2. x < y
3. x ≥ y
4. x ≤ y
5. x = y or relationship between x and y cannot be established

Answer 1

Correct Answer - Option 4 : x ≤ y

I. \(3{x^2} - 22x + 7 = 0\)

\( \Rightarrow 3{x^2} - x - 21x + 7 = 0\)

\( \Rightarrow x\left( {3x - 1} \right) - 7\left( {3x - 1} \right) = 0\)

\( \Rightarrow \left( {x - 7} \right)\left( {3x - 1} \right) = 0\)

\( \Rightarrow x = 7\) or \(\frac{1}{3}\)

 

II. \({y^2} - 20y + 91 = 0\)

\( \Rightarrow {y^2} - 13y - 7y + 91 = 0\)

\( \Rightarrow y\left( {y - 13} \right) - 7\left( {y - 13} \right) = 0\)

\( \Rightarrow \left( {y - 7} \right)\left( {y - 13} \right) = 0\)

\( \Rightarrow y = 7\) or 13

Comparison between x and y (via Tabulation):

Value of x	Value of y	Relation
7	7	x = y
7	13	x < y
1/3	7	x < y
1/3	13	x < y

∴ Clearly \(x \le y\)