Question

If a2 +b2 = 34 and ab=15 , find the values of a+b and a-b.

Answer 1

a+b=8
a-b=2 thats the right answer

Answer 2

The values of  "a + b = 8"  and "a - b = 2".

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.