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MissTica
3 years ago
12

Given that a - b = 3 and ab=5, find, without the use of a calculator, the value of a +b?

Mathematics
1 answer:
Angelina_Jolie [31]3 years ago
4 0

Answer:

√29

Step-by-step explanation:

We are here given that ,

  • a - b = 3
  • ab = 5 .

Now square the first equation ,

⇒ a - b = 3

⇒ ( a - b)² = 3²

⇒ a² + b² - 2ab = 9

⇒ a² + b² - 2(5) = 9

⇒ a² + b² -10 = 9

⇒ a² + b² = 9 + 10

⇒ a² + b² = 19

  • Adding 2ab both sides ,

⇒ a² + b² + 2ab = 19 + 2(5)

⇒ (a + b)² = 19 + 10

⇒ ( a + b)² = 29

⇒ a + b = √29 .

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