Question
When the sum of the squares of two positive integers is
given as 1,600, and their product is given as 768. Determine the value of the smaller integer.Solution
ATQ, Let, the two numbers be 'm' and 'n', such that, 'm > 'n'. ATQ, m 2 + n2 = 1600 And, m × n = 768 We know that, (a + b)2 = a2 + b2 + 2ab, and, (a - b)2 = a2 + b2- 2ab So, (m + n)2 = 1600 + 2 × 768 Or, (m + n)2 = 1600 + 1536 Or, (m + n)2 = 3136 Since both the numbers are greater than zero. So, m + n = 56 ....(i) Similarly, (m - n)2 = m2 + n2- 2mn So, m - n = 8 ....(ii) On subtracting equation (ii) from equation (i) , we get, 2n = 48 So, n = 24 So, the value of the smaller number = n = 24
What approximate value will come in place of the question mark (?) in the following question? (Note: You are not expected to calculate the exact value.)...
(1488.06 × 4.99) - 5677.95 + 1038.06 - 658.97 + (272.95 × 3.05) = ? × (36.95 × 4.02)
11.69% of 499.78 + (2.89 × 39.76) = ?Â
6401.23 × `1 3/4` - 352.87 × ? = 10443.789
What approximate value should come in the place of (?) in the following questions?
...
713.92 ÷ 14.14 * 69.8 = ? * 20.74 ÷ 8.9What approximate value will replace the question mark (?) in the following?
√57...
What approximate value will come in place of the question mark (?) in the following question? (Note: You are not expected to calculate the exact value.)...
600.11 ÷ 14.98 x 5.14 – 171.9 = √?Â
What approximate value will come in place of the question mark (?) in the following question? (Note: You are not expected to calculate the exact value.)...
? = 25.08 + 11.99 × 24.07
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