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If X lies between -3 and -1 and Y lies between -1 and 1, then X2 – Y2 lies between which two values?

If X lies between -3 and -1 and Y lies between -1 and 1, then X2 – Y2 lies between which two values? Correct Answer 1 and 8

Given:

X lies between -3 and -1 and Y lies between -1 and 1.

Concepts used:

a2 – b2 = (a – b) × (a + b)

Calculation:

-3 ≤ X ≤ -1

⇒ 1 ≤ X2 ≤ 9

-1 ≤ Y ≤ 1

⇒ 0 ≤ Y2 ≤ 1

⇒ 1 – 0 ≤ X2 – Y2 ≤ 9 – 1

⇒ 1 ≤ X2 – Y2 ≤ 8

∴ Expression X2 – Y2 lies between 1 and 8.

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