Question

find the value of a + b if a2(a square) + b2(b square)= 34 and ab = 15​

Answer 1

Answer:

Step-by-step explanation:

We have,

a^{2} +b^{2} =34 and ab=15

To find, the values of  a + b and a - b = ?

∴(a+b)^{2} =a^{2}+b^{2}+2ab

⇒ (a+b)^{2} =34+2(15)=34+30=64

⇒ (a+b)^{2}=8^{2}

⇒ a + b = 8      .....(1)

Also,

(a-b)^{2} =(a+b)^{2} -4ab

From (1), we get

(a-b)^{2} =(8)^{2} -4(15)=64-60=4

⇒ (a-b)^{2}=2^{2}

⇒ a - b = 2

Hence, the values of  a + b = 8  and a - b = 2.

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Answer 2

We have  a²+b² =34 and ab=15.

(a+b)² = a²+b²+2ab

⇒ (a+b)² = 34+2×15

⇒ (a+b)² = 64

⇒ (a+b)² = 8²

⇒ a+b = 8

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