Question

if a^2+b^2=9 and ab=4.
Find the value of 3(a+b)^2 - 2(a-b)^2.

Answer 1

Hi ,

a² + b² = 9 -----( 1 )

ab = 4 ----( 2 )

i ) ( a + b )² = a² + b² + 2ab

= 9 + 2 × 4

= 9 + 8

= 17 ---( 3 )

ii ) ( a - b )² = a² + b² - 2ab

= 9 - 2 × 4

= 9 - 8

= 1 ---( 4 )

From ( 3 ) & ( 4 ) ,

Value of 3( a + b )² - 2 ( a - b )²

= 3 × 17 - 2 × 1

= 51 - 2

= 49

I hope this helps you.

: )

Answer 2

Howdy!!

your answer is ---

Given, ab = 4

${a}^{2} + {b}^{2} = 9 \\ = > {(a + b)}^{2} - 2ab = 9 \\ = > {(a + b)}^{2} - 2 \times 4 = 9 \\ = > {(a + b)}^{2} = 17......(1)$

now,
$3 {(a + b)}^{2} - 2 {(a - b)}^{2} \\ = 3 {(a + b)}^{2} - 2 {(a + b)}^{2} - 4ab \\ = 3 \times 17 - 2(17 - 4 \times 4) \\ = 51-2= 49$

hope it help you