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Sum of the numbers = 13 × 2 = 26 Let the two numbers be a and b So, (a + b) = 26 ----(i) Now, √ab = 12 ⇒ (√ab)2 = 122 ⇒ ab = 144 Now, (a + b)2 = 262 ⇒ a2 + b2 + 2ab = 676 ⇒ a2 + b2 + 2ab - 4ab = 676 - 4 × 144 ⇒ a2 + b2 - 2ab = 676 - 576 ⇒ (a - b)2 = 100 ⇒ (a - b) = 10 ----(ii) From eq (i) and eq (ii) we can say a = 18 and b = 8 Now, Difference of the two numbers = 18 - 8 ⇒ 10 ∴ The difference between the numbers is 10.
Four terms are in proportion. The first, second and fourth terms are 4, 22, and 33. Find the third term.
3 2 2 3 8 ?
...31 33 69 212 ? 4286
...1 2 6 ...
13, 14, 18, 27, 43, ?
104 136 152 160 164 ?
...4 7 24 91 462 2763
18 ...
123 125 129 132 ? 145
42 43 46 ...
2342 2223 2090 1943 1782 ?
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