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

I. \({x^2} - 11x + 30 = 0\)

II. \(2{y^2} - 12y + 10 = 0\)


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

1 Answer

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Correct Answer - Option 3 : x ≥ y

I. \({x^2} - 11x + 30 = 0\)

\( \Rightarrow {x^2} - 5x - 6x + 30 = 0\)

\( \Rightarrow x\left( {x - 5} \right) - 6\left( {x - 5} \right) = 0\)

\( \Rightarrow \left( {x - 6} \right)\left( {x - 5} \right) = 0\)

\( \Rightarrow x = 6\) or 5

 

II. \(2{y^2} - 12y + + 10 = 0\)

\( \Rightarrow 2{y^2} - 2y - 10y + 10 = 0\)

\( \Rightarrow 2y\left( {y - 1} \right) - 10\left( {y - 1} \right) = 0\)

\( \Rightarrow \left( {y - 1} \right)\left( {2y - 10} \right) = 0\)

\( \Rightarrow \left( {y - 1} \right)\left( {y - 5} \right) = 0\)

\( \Rightarrow y = 1\) or 5

Comparison between x and y (via Tabulation):

Value of x

Value of y

Relation

6

1

x > y

6

5

x > y

5

1

x > y

5

5

x = y


∴ Clearly \(x \ge y\)

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