Question

if if a a is equals to 10 and b e is equals to 5 find a square minus b square​

Answer 1

Given:

a² + b² = 9 and ab = 4

To find: Value of 3( a + b)² - 2( a - b )²

Consider the identity,

( a - b )² = a² + b² - 2ab

( a - b )² = 9 - 2 × 4

( a - b )² = 9 - 8

( a - b )² = 1

( a - b ) = ± √1

Now, Consider another identity

( a + b )² = a² + b² + 2ab

( a + b )² = 9 + 2 × 4

( a + b )² = 9 + 8

( a + b )² = 17

( a + b ) = ± √17

Finally consider,

3( a + b )² - 2( a - b )²

= 3( ± √17 )² - 2( ± √1 )²

= 3 × 17 - 2 × 1

= 51 - 2

= 49

Therefore, Value of the given Expression is 49.

$\color{blue}{ Answered \ by \ Srijan}$

Answer 2

Given,

⇒a+b=10

⇒ab=16

⇒(a+b)^2

=a^2+b ^2 +2ab

⇒10^2

=a^2+b ^2 +2(16)

∴a^2 +b^2

=68

⇒a^2+b^2

+ab=68+16=84

⇒a^2+b^2

−ab=68−16=52