Question

find the value of 8ab (a2+b2) when a+b=-5 and a-b=5​

Answer 1

Solution :

(a+b) = -5 and (a-b) = 5

Adding these two equations

>> 2a + b - b = -5 + 5 = 0

>> 2a = 0

>> a = 0

& b = -5

To find :

The value of 8ab(a² + b²)

> 8 × 0 × -5 ( 0 + 25)

> 0

This is the required answer.

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Additional Information :

(a + b)² = a² + 2ab + b²

(a + b)² = (a - b)² + 4ab

(a - b)² = a² - 2ab + b²

(a - b)² = (a + b)² - 4ab

a² + b² = (a + b)² - 2ab

a² + b² = (a - b)² + 2ab

2 (a² + b²) = (a + b)² + (a - b)²

4ab = (a + b)² - (a - b)²

ab = {(a + b)/2}² - {(a-b)/2}²

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

(a + b)³ = a³ + 3a²b + 3ab² b³

(a + b)³ = a³ + b³ + 3ab(a + b)

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)( a² - ab + b² )

a³ + b³ = (a + b)³ - 3ab( a + b)

a³ - b³ = (a - b)( a² + ab + b²)

a³ - b³ = (a - b)³ + 3ab ( a - b )

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Answer 2

Appropriate Question :

find the value of 8ab (a² + b²) when a + b= -5 and a - b = 5

How to do :

1) We need to get the value of a² + b² using (a + b)² + (a - b)² = 2(a² + b²)

2) We need to find the value of ab using (a + b)² - (a - b)² = 4ab

3) Then putting those values in 8ab (a² + b²) we can find the answer

Formula Used :

• (a + b)² + (a - b)² = 2(a² + b²)

• (a + b)² - (a - b)² = 4ab

Solution :

We have been provided with the values of a + b and a - b

Using the identity (a + b)² + (a - b)² = 2(a² + b²) we get

• (a + b)² + (a - b)² = 2(a² + b²)

Putting the values we get

• ( -5)² + (5)² = 2(a² + b²)

• 25 + 25 = 2(a² + b²)

Transposing 2 on the right hand side we get

• 50/2 = a² + b²

• a² + b² = 25

∴ The value of a² + b² is 25

Now to find ab

For ab we need to apply (a + b)² - (a - b)² = 4ab

• (a + b)² - (a - b)² = 4ab

Inserting the values we find :

• ( -5)² - (5)² = 4ab

• 25 - 25 = 4ab

• 0/4 = ab

• ab = 0

∴ The value of ab is 0

According to the given question we need to find 8ab (a² + b²)

• 8ab (a² + b²)

Putting the values we have :

• 8 × 0 ( 25)²

• 0 × 625

• 0

∴ The value of 8ab (a² + b²) is 0

$\underline{ \boxed{ \mathcal{\dag \:\red{ KNOW} \: \green{MORE \: \dag}}}}$

$\sf \looparrowright {(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2}$

$\sf \looparrowright {a}^{2} + {b}^{2} = {(a + b)}^{2} - 2ab$

$\sf \looparrowright {(a - b)}^{2} = {a}^{2} - 2ab + {b}^{2}$

$\sf \looparrowright {a}^{2} + {b}^{2} = {(a - b)}^{2}$

$\sf \looparrowright(a - b)(a + b) = {a}^{2} - {b}^{2}$

$\sf \looparrowright {(a + b)}^{2} + {(a - b)}^{2} = 2( {a}^{2} + {b}^{2} )$

$\sf \looparrowright {(a + b)}^{2} - {(a - b)}^{2} = 4ab$

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# BeBrainly