Question

if a-b = 4 and ab = 52.25 then a2-b2 is

Answer 1

Answer:

60

Step-by-step explanation:

please see the picture

Answer 2

Answer :

$\large{\star\:\:\boxed{\bf{a^2\:-\:b^2\:=\:60}}\:\:\star}$

Explanation :

Given :–

• a - b = 4

• ab = 52.25

To Find :–

• The value of a² - b² .

Formula Applied :–

• $\boxed{\star\:\:\bf{(a\:+\:b)^2\:=\:(a\:-\:b)^2\:+\:4ab}\:\:\star}$

• $\boxed{\star\:\:\bf{a^2\:-\:b^2\:=\:(a\:+\:b)(a\:-\:b)}\:\:\star}$

Solution :–

We have ,  

• a - b = 4

• ab = 52.25

Putting these values in the Formula :-

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

$\rightarrow\sf{(a\:+\:b)^2\:=\:(4)^2\:+\:4(52.25)}$

$\rightarrow\sf{(a\:+\:b)^2\:=\:16\:+\:209}$

$\rightarrow\sf{(a\:+\:b)^2\:=\:225}$

$\rightarrow\sf{a\:+\:b\:=\:\sqrt{225}}$

$\rightarrow\bf{a\:+\:b\:=\:15}$

Now we have ,

• a + b = 15
• a - b = 4

Putting these values in the Formula :

$\rightarrow\sf{a^2\:-\:b^2\:=\:(a\:+\:b)(a\:-\:b)}$

$\rightarrow\sf{a^2\:-\:b^2\:=\:(15)(4)}$

$\rightarrow\boxed{\bf{a^2\:-\:b^2\:=\:60}}$

∴ The value of a² - b² is 60 .

→ What do you need to know ?

➤ You need to know that how (a + b)² and (a - b)² +4ab are Equal ?

Answer :-

Let's first open the Brackets by applying the Appropriate Formula :

➼ (a² + 2ab + b²) = (a² - 2ab + b²) + 4ab

➼ a² + 2ab + b² = a² -2ab + 4ab + b²

➼ a² + 2ab + b² = a² + 2ab + b²

➼ LHS = RHS

Hence Proved .