Question

If a + b = 4 and ab = -12, find a-b and a+b​

Answer 1

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Answer 2

Step-by-step explanation:

Answer :

\large{\star\:\:\boxed{\bf{a^2\:-\:b^2\:=\:60}}\:\:\star}⋆a2−b2=60⋆

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}⋆(a+b)2=(a−b)2+4ab⋆

\boxed{\star\:\:\bf{a^2\:-\:b^2\:=\:(a\:+\:b)(a\:-\:b)}\:\:\star}⋆a2−b2=(a+b)(a−b)⋆

Solution :–

We have ,  

a - b = 4

ab = 52.25

Putting these values in the Formula :-

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

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

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

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

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

\rightarrow\bf{a\:+\:b\:=\:15}→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)}→a2−b2=(a+b)(a−b)

\rightarrow\sf{a^2\:-\:b^2\:=\:(15)(4)}→a2−b2=(15)(4)

\rightarrow\boxed{\bf{a^2\:-\:b^2\:=\:60}}→a2−b2=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 .