Question

a-b=5 , a^3-b^3=1280,a^2-b^2=​

Answer 1

Step-by-step explanation:

Given:-

a-b=5

a^3-b^3=1280

To find:-

Find the value of a^2-b^2 ?

Solution:-

Given that

a - b = 5 ----------------(1)

a^3 - b^3 = 1280------(2)

We know that

a^3-b^3 = (a-b)^3 +3ab(a-b)

From (1)&(2)

=> 1280 = (5)^3 +3ab(5)

=> 1280 = 125+15ab

=> 1280-125 = 15 ab

=> 1155 = 15ab

=> 15ab = 1155

=> ab = 1155/15

ab = 77-----------------(3)

We know that

(a+b)^2 = (a-b)^2+4ab

From (1) and (3)

=> (a+b)^2 = (5)^2+4(77)

=> (a+b)^2 = 25+308

=> (a+b)^2 =333

=> a+b =√333 ---------(4)

Now the value of a^2-b^2

=>(a+b)(a-b)

From (1) and (4)

=> 5(√333)

=> 5√333

or

=> √(333×25)

=>√8325

Answer:-

The value of a^2-b^2 for the given problem is

√8325 or 5√333

Used formulae:-

• a^3-b^3 = (a-b)^3 +3ab(a-b)
• a^2-b^2=(a+b)(a-b)
• (a+b)^2 = (a-b)^2+4ab