Question

a² + b² = 7b and b² + (2b-a)² = 7² find (a - b)² .

Answer 1

Answer:

( a - b )² =  1.27825.

Explanation:

Given :

a² + b² = 7 b

a² = 7 b - b²

a = √ ( 7 b - b² )

Also given :

b² + ( 2 b - a )² = 7²

⇒ b² + 4 b² + a² - 4 a b = 7²

4 b² + 7 b - 7² = 4 a b   [ a² + b² = 7 b ]

Putting value of a = √ ( 7 b - b² )

4 b² + 7 b - 7² = 4 b √ ( 7 b - b² )

Squaring on both side :

( 4 b² + 7 b - 49 )² = ( 4 b √ ( 7 b - b² ) )²

( 16 b⁴ + 49 b²  + 49²  + 56 b³ - 49 × 14 b - 49 × 8 b² ) = 16 b² ( 7 b - b² )

16 b⁴ + 49 b²  + 49²  + 56 b³ - 49 × 14 b - 49 × 8 b² ) = 112 b³ - 16 b⁴

32 b⁴  - 56 b³ + 2401 + 49 b² - 686 b - 392 b² = 0

32 b⁴  - 56 b³ - 343 b² - 686 b + 2401 = 0

On solving bi-quadratic equation we get :

Real part :

b ≈ 4.4806

b ≈ 1.8373

Also complex part :

b ≈ -2.2480 - 2.0517 i

b ≈ 2.2480 + 2.0517 i

Taking real part and finding value of 'a' :

a = √ [ ( b ( 7 - b ) ]

When b = 4.4806

a = √ [ 4.4806 ( 7 - 4.4806 ) ]

a = 3.35

When b = 1.8373

a = √ [ 1.8373 ( 7 - 1.8373 )

a = 3.0798

Now :

( a - b )² = ( 3.35 - 4.4806 )²

= > 1.27825

Therefore the value of ( a - b )² is  1.27825.

Answer 2

Refer to the attachment ✔️✔️✔️✔️✔️✔️