Question

$if \: a \: - b = 16 \: and \: {a}^{2} + {b}^{2} = 400. \: find \: ab$
​

Answer 1

Given:-

→ Value of (a - b) is 16 .

→ Value of (a² + b²) is 400.

To find:-

→ Value of ab.

Solution:-

In order to solve this problem, we have to use the identity :-

(a - b)² = a² + b² - 2ab

Now by substituting values in the above identity, we get :-

⇒ (16)² = 400 - 2ab

⇒ 256 = 400 - 2ab

⇒ 256 - 400 = -2ab

⇒ -144 = -2ab

⇒ ab = -144/-2

⇒ ab = 72

Thus, value of 'ab' is 72 .

Some Extra Information:-

Some algebraic identities that are used to solve these kinds of problems are :-

• (a + b)² = a² + b² + 2ab

• (a² - b²) = (a + b)(a - b)

• (a + b)³ = a³ + b³ + 3ab(a + b)

• (a - b)³ = a³ - b³ - 3ab(a - b)

Answer 2

Given :-

• a - b = 16

• a² + b ² = 400

To find :-

• ab.

Solution :-

$\large\star{\boxed{\sf{\blue{ ( a - b) ² = a² + b² - 2ab}}}}$

$\tt{ ⟹ \ ( 16 )² \ = \ 400 \ - \ 2ab}$

$\tt{⟹ \ 256 \ = \ 400 \ - \ 2ab}$

$\tt{⟹ \ 256 \ - \ 400 \ = \ - \ 2ab }$

$\tt{⟹ \ - 144 \ = \ - 2ab }$

$\tt{⟹ \ ab \ = \ 72}$

$\rm\bigstar\purple{ \ Ab \ = \ 72}$