A² + b² = 7b and b² + (2b-a)² = 7² find (a - b)² .
Answers
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.
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