While multiplying three real numbers, Ashok took one of the numbers as 73 instead of 37. As a result, the product went up by 720. Then the minimum possible value of the sum of squares of the other two numbers is
Explanation:
Let X and Y are the two real numbers.
X × Y × 73 − X × Y × 37 = 720
X × Y × (73 – 37) = 720
X × Y × 36 = 720
X × Y = 20
AM(X2, Y2) ≥ GM(X2, Y2)
∴ X2+Y22 ≥ X2×Y2
∴ (X2 + Y2) ≥ 40
Alternately, We know, X × Y = 40
Also, (X - Y)2 ≥ 0 [Square of any number is always greater than or equal to zero]
∴ X2 + Y2 - 2XY ≥ 0
∴ X2 + Y2 ≥ 2XY
∴ X2 + Y2 ≥ 40
Hence, 40.
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