Question

a-b=4 and ab=45 then find (a+b)^2

Answer 1

given a-b=4
squaring on both sides
(a-b)²=16
a²+b²-2ab=16
adding 4ab on both sides
a²+b²+2ab=16+4ab
given ab=45
(a+b)²=16+4(45)
(a+b)²=196
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Answer 2

The value of $(a+b)^{2}=196.$

Step-by-step explanation:

We have,

a - b = 4 and ab = 45

To find, the vaue of $(a+b)^{2} =?$

We know that,

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

Put a - b = 4 and ab = 45, we get

$(a+b)^{2} =4^{2} +4(45)$

⇒ $(a+b)^{2} =16 +180=196$

∴ $(a+b)^{2}=196$

Hence, the value of $(a+b)^{2}=196.$