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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. \({x^2} - 14x + 48 = 0\)

II. \({y^2} - 16y + 63 = 0\)


1. x > y
2. x < y
3.

x ≥ y


4.

x ≤ y


5.

x = y or relationship between x and y cannot be established

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Best answer
Correct Answer - Option 5 :

x = y or relationship between x and y cannot be established


I.\({x^2} - 14x + 48 = 0\)

\( ⇒ {x^2} - 6x - 8x + 48 = 0\)

\( ⇒ x\left( {x - 6} \right) - 8\left( {x - 6} \right) = 0\)

\( ⇒ \left( {x - 6} \right)\left( {x - 8} \right) = 0\)

⇒ x = 6  or 8

 

II. \({y^2} - 16y + 63 = 0\)

\( ⇒ {y^2} - 9y - 7y + 63 = 0\)

\( ⇒ y\left( {y - 9} \right) - 7\left( {y - 9} \right) = 0\)

\( ⇒ \left( {y - 7} \right)\left( {y - 9} \right) = 0\)

⇒ y = 7  or 9

Comparison between x and y (via Tabulation):

Value of x

Value of y

Relation

6

7

x < y

6

9

x < y

8

7

x > y

8

9

x < y


∴ x = y or relationship between x and y cannot be established

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