Question

a+b= 4 and ab = -12 find a²-b²​

Answer 1

Answer:

Answer :-

To find a² - b²

a + b = 4

ab = -12

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Use indentity :-

(a + b)² = a² + b² + 2ab

=> 4² = a² + b² + 2 × (-12)

=> 16 + 24 = a² + b²

=> 40 = a² + b²

use identity of (a - b)² = a² + b² - 2ab

=>(a - b)² = 40 - 2 × (-12)

=> (a - b)² = 40 + 24

=> ( a - b)² = 64

=> a - b = 8

Now = a² - b² = (a + b)(a - b)

=> 4 × 8

=> 32

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Hope it's helpful

Thank you

Answer 2

Question:-

• If a + b = 4 and ab = - 12 then find the value of a² - b²

To Find:-

• Find the value of a² - b²

Solution:-

$\sf\longrightarrow \: a + b = 4$

$\sf\longrightarrow \: b = 4 - a . . . . . ( i )$

$\sf\longrightarrow \: ab = - 12$

$\sf\longrightarrow \: a( 4 - a ) = - 12$

$\sf\longrightarrow \: 4a - a^2 = - 12$

$\sf\longrightarrow \: a^2 - 4a - 12 = 0$

$\sf\longrightarrow \: a^2 - 6a + 2a - 12 = 0$

$\sf\longrightarrow \: a( a - 6 ) + 2( a - 6 ) = 0$

$\sf\longrightarrow \: ( a - 6 ) ( a + 2 )$

$\sf\longrightarrow \: a = 6 ; - 2$

If a = 6 then the value of b is:-

$\sf\longrightarrow \: b = 4 - a$

$\sf\longrightarrow \: b = 4 - 6$

$\sf\longrightarrow \: b = - 2$

If a = - 2 then the value of b is:-

$\sf\longrightarrow \: b = 4 - a$

$\sf\longrightarrow \: b= 4 - ( - 2 )$

$\sf\longrightarrow \: b = 4 + 2$

$\sf\longrightarrow \: b = 6$

Then, now we have to find the value of a² - b²:-

• If a = 6 and b = - 2

$\sf\longrightarrow \: { a }^{ 2 } - { b }^{ 2 }$

$\sf\longrightarrow \: 6^2 - { ( - 2 ) }^{ 2 }$

$\sf\longrightarrow \: 36 - 4$

$\sf\longrightarrow \: 32$

Then, now we have to find the value of a² - b²:-

If a = - 2 and b = 6

$\sf\longrightarrow \: { a }^{ 2 } - { b }^{ 2 }$

$\sf\longrightarrow \: { ( - 2 ) }^{ 2 } - { 6 }^{ 2 }$

$\sf\longrightarrow \: 4 - 36$

$\sf\longrightarrow \: - 32$

Hence ,

• The value of ± 32