Question

If a + b = 8 and ab =15 , find a2 + b2
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Answer 1

Answer:

34

Step-by-step explanation:

algebraic identity for (a+b)² =a²+b²+2ab

we know that a+b=8 and ab=15

so thus substituting we get=

8²=a²+b2+2x15

64=a²+b²+30

so a²+b²=64-30=34

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Answer 2

Answer:

Step-by-step explanation:

ANSWER:-

Given that:-

• a+b = 8
• ab = 15

To find:-

$\rm{a^2+b^2}$

Let's Do!

For finding the answer, we need to know one identity.

$\rm{a^2+b^2 = (a+b)^2-2ab}$

$\rm{a^2+b^2 = (a-b)^2+2ab}$

We will use the first identity, as information is given for that.

$\rm{a^2+b^2 = (a+b)^2-2ab}$

$\rm{a^2+b^2 = (8)^2-2(15)}$

$\rm{a^2+b^2 = 64-30}$

$\boxed{\rm{a^2+b^2 = 34}}$

So, 34 is the required answer.

Some more Identities:-

$\rm{(a+b)^2 = a^2+b^2+2ab}$

$\rm{(a-b)^2 = a^2+b^2-2ab}$

$\rm{a^2+b^2 = (a+b)^2-2ab \ OR \ a^2+b^2 = (a-b)^2+2ab}$

$\rm{a^2-b^2 = (a-b)(a+b)}$