Question

if a+b=5 and a-b = √17 then the value
of ab should be​

Answer 1

Given :  a+b=5 and a-b = √17

To Find : Value of ab

Solution:

Method 1

a+b=5  

a-b = √17

Adding both

=> 2a = 5 + √17

Subtracting

2b = 5 - √17

(2a)(2b) = (5 + √17)(5 - √17)

=> 4ab = 25 - 17

=> 4ab = 8

=> ab = 2

Method 2

a+b=5  

a-b = √17

Squaring both side

=> a² + b² + 2ab = 25

   a² + b² - 2ab =  17

=> 4ab = 8

=> ab = 2

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Answer 2

SOLUTION

GIVEN

a + b = 5 and a-b = √17

TO DETERMINE

The value of ab

FORMULA TO BE IMPLEMENTED

We are aware of the formula that

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

EVALUATION

Here it is given that a+b=5 and a-b = √17

Now

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

$\sf{ \implies \: 4ab = {(5)}^{2} - {( \sqrt{17} )}^{2} }$

$\sf{ \implies \: 4ab = 25 - 17 }$

$\sf{ \implies \: 4ab = 8}$

$\sf{ \implies \: ab = 2 }$

FINAL ANSWER

Hence the required value of ab = 2

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