The sum of the age of sonam and geetha is twice the sum of their ages 7 years ago.What is the product of their present ages,if the sum of the squares of their ages,7 years ago was 100.
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Answer:
99 yrs²
Step-by-step explanation:
Present age of Sonam = s
Present age of Geetha = g
According to question
s + g = 2[(s - 7) + (g - 7)]
s + g = 2(s + g - 14)
s + g = 2s + 2g - 28
s + g = 28
Also, it's given that
(s - 7)² + (g - 7)² = 100
From (a + b)² = a² + b² + 2ab
a² + b² = (a + b)² - 2ab
(s - 7 + g - 7)² - {2 × [(s - 7) × (g - 7)]} = 100
(s + g - 14)² - {2 × [s(g - 7) - 7(g - 7)]} = 100
(28 - 14)² - {2 × [sg - 7s - 7g + 49]} = 100
14² - [2 × (sg - 7(s + g - 7)] = 100
196 - [2 × (sg - 7(28 - 7)] = 100
2(sg - 7(21)) = 100 - 196
sg - 147 = -96/2
sg = 147 - 48
sg = 99
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