Question

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

I. \({x^2} - 22x + 117 = 0\)

II. \({y^2} + 4y - 96 = 0\)

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 1 : x > y

I. \({x^2} - 22x + 117 = 0\)

\( \Rightarrow {x^2} - 13x - 9x + 117 = 0\)

\( \Rightarrow x\left( {x - 13} \right) - 9\left( {x - 13} \right) = 0\)

\( \Rightarrow \left( {x - 13} \right)\left( {x - 9} \right) = 0\)

\( \Rightarrow x = 9\) or 13

 

II. \({y^2} + 4y - 96 = 0\)

\( \Rightarrow {y^2} + 12y - 8y - 96 = 0\)

\( \Rightarrow y\left( {y + 12} \right) - 8\left( {y + 12} \right) = 0\)

\( \Rightarrow \left( {y - 8} \right)\left( {y + 12} \right) = 0\)

\( \Rightarrow y = - 12\) or 8

Comparison between x and y (via Tabulation):

Value of x	Value of y	Relation
9	-12	x > y
9	8	x > y
13	-12	x > y
13	8	x > y

∴ Clearly x > y