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प्रश्न
The area of a circle is given by the expression πx2 + 6πx + 9π. Find the radius of the circle.
उत्तर
We have,
Area of a circle = πx2 + 6πx + 9π = π(x2 + 6x + 9)
⇒ πr2 = π(x2 + 3x + 3x + 9) ...[∵ Area of a circle = πr2, where r is the radius]
⇒ πr2 = π[x(x + 3) + 3(x + 3)] = π(x + 3)(x + 3) = π(x + 3)2
⇒ πr2 = π(x + 3)2
On comapring both sides, r2 = (x + 3)2 ⇒ r = x + 3
Hence, the radius of circle is x + 3.
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