Question

⚠️Kindly Don't spamm⚠️
– Non-copied Answer
– Well-explained Answer

​

Answer 1

(a)

GIVEN :–

$\\ \tt \implies x {y}^{2} k = {(4xy + 3y)}^{2} - {(4xy - 3y)}^{2}$

TO FIND :–

• Value of 'k' = ?

SOLUTION :–

$\\ \tt \implies x {y}^{2} k = {(4xy + 3y)}^{2} - {(4xy - 3y)}^{2}$

• Using identity –

$\\ \tt \implies {(a)}^{2} - {(b)}^{2} = (a + b)(a - b)$

• So that –

$\\ \tt \implies x {y}^{2} k = {(4xy + 3y + 4xy - 3y)} {(4xy + 3y - \{4xy - 3y \})}$

$\\ \tt \implies x {y}^{2} k = {(4xy + 4xy )} {(4xy + 3y - 4xy + 3y)}$

$\\ \tt \implies x {y}^{2} k = {(8xy)} {(3y + 3y)}$

$\\ \tt \implies x {y}^{2} k = {(8xy)} {(6y)}$

$\\ \tt \implies x {y}^{2} k =48x {y}^{2}$

$\\ \tt \implies k = \dfrac{48x {y}^{2}}{x {y}^{2}}$

$\\ \large \implies{ \boxed{ \tt k = 48}}$

▪︎ Hence , The value of k is 48.

$\\\rule{220}{2}$

(b)

GIVEN :–

$\\ \tt \implies {a}^{2} + {b}^{2} = 9 \: \: and \: \: ab = 4$

TO FIND :–

$\\ \tt \implies Value \: \: of \: \: 3 {(a + b)}^{2} - 2(a - b)^{2} =?$

SOLUTION :–

• Let –

$\\ \tt \implies P = 3 {(a + b)}^{2} - 2(a - b)^{2}$

• Using identity –

$\\ \tt \implies (a \pm b)^{2} = {a}^{2} + {b}^{2} \pm2ab$

• So that –

$\\ \tt \implies P = 3[{a}^{2} + {b}^{2} + 2ab]- 2[{a}^{2} + {b}^{2} - 2ab]$

• Put the values –

$\\ \tt \implies P = 3[9+2(4)]- 2[9 - 2(4)]$

$\\ \tt \implies P = 3(9+8)- 2(9 -8)$

$\\ \tt \implies P = 3(17)- 2(1)$

$\\ \tt \implies P =51- 2$

$\\ \large\implies{ \boxed{ \tt P =49}}$

Answer 2

Answer:

❖ 1) ✯ Given :-

• xy²k = (4xy + 3y)² - (4xy - 3y)²

✯ To Find :-

• What is the value of k.

✯ Solution :-

➙ xy²k = (4xy + 3y)² - (4xy - 3y)²

⇒ xy²k = 16x²y² + 9y² + 24xy² - (16x²y² + 9y² - 24xy²)

⇒ xy²k = 16x²y² + 9y² + 24xy² - 16x²y² - 9y² + 24xy²

⇒ xy²k = 48xy²

➥ k = 48

$\therefore$ The value of k is $\boxed{\bold{\large{48}}}$

_______________________________

❖ 2) ✯ Given :-

• a² + b² = 9 and ab = 4

✯ To Find :-

• What is the value of 3(a + b)² - 2(a - b)²

✯ Solution :-

➙ 3(a + b)² - 2(a - b)²

⇒ 3(a² + b² + 2ab) - 2(a² + b² - 2ab)

⇒ 3a² + 3b² + 6ab - 2a² - 2b² + 4ab

⇒ a² + b² + 10ab

» Putting a² + b² = 9 and ab = 4 we get,

⇒ 9 + 10(4)

⇒ 9 + 40

➥ 49

$\therefore$ The value of 3(a + b)² - 2(a - b)² is $\boxed{\bold{\small{49}}}$

_______________________________