Question

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

Answer 1

Given :

• a + b = 5
• a - b = √17

To find :

• The value of ab

Formula used :

• $\rm{4ab=\boxed{(a+b)^2-(a-b)^2}}$

Now by substituting the values,we get

$\begin{gathered}\:\:\:\:\:\displaystyle{\sf{\leadsto\:4ab=(5)^2-(√17)^2}}\end{gathered}$

$\begin{gathered}\:\:\:\:\:\displaystyle{\sf{\leadsto\;4ab=25-17}}\end{gathered}$

$\begin{gathered}\:\:\:\:\:\displaystyle{\sf{\leadsto\;4ab=8}}\end{gathered}$

$\begin{gathered}\:\:\:\:\:\displaystyle{\sf{\leadsto\;ab=\cancel\frac{8}{4}}}\end{gathered}$

$\begin{gathered}\:\:\:\:\:\displaystyle{\sf{\leadsto\;ab=2}}\end{gathered}$

Basic formulas to know:

• (a+b)² = a² + b² + 2ab
• (a-b)² = a² + b² - 2ab
• (a+b+c)² = a² + b² +c²+2(ab+bc+ca)
• a²-b²=(a+b)(a-b)
• ${ab=(\frac{a+b}{2})^2-(\frac{a-b}{2})^2}$

Answer 2

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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