Math, asked by GREATBEAST1446, 1 year ago

Solve the equation (6-x)4+(8-x)4=16.(ans : x=8 or x=6)

Answers

Answered by amitnrw
25

Answer:

x = 6 & 8

Step-by-step explanation:

(6-x)⁴ + (8-x)⁴  = 16

=> (6-x)⁴+ ((8-x)²)² = 16

=> (6-x)⁴ +  ((8-x)²)² - 4² = 0

=> (6-x)⁴  + ( (8-x)² + 4)((8-x)² - 4) = 0

=> (6-x)⁴ + (x² + 64 - 16x + 4)((8-x + 2)(8-x -2) = 0

=> (6-x)⁴  + (x² + 64 - 16x + 4)((10-x)(6-x) = 0

=> (6-x)  ( (6-x)³  + (x² + 68 - 16x)(10-x) = 0

=> x = 6

(6-x)³  + (x² + 68 - 16x)((10-x) = 0

=> 216 - x³ -108x  +18x² -x³ +26x² -228x + 680 = 0

=> -2x³ + 44x² -336x + 896 = 0

=> x³ - 22x² + 168x - 448 = 0

=> (x -8)(x² - 14x + 56) = 0

=> x = 8

or similialr to 1st step :

(6-x)⁴ + (8-x)⁴  = 16

=> (6-x)⁴+ ((8-x)²)² = 16

=>  (8-x)⁴  +  ((6-x)²)² - 4² = 0

=>(8-x)⁴  + ( (6-x)² + 4)((6-x)² - 4) = 0

=>(8-x)⁴+ (x² + 36 - 12x + 4)((6-x + 2)(6-x -2) = 0

=> (8-x)⁴ + (x² + 40 - 12x)((8-x)(4-x) = 0

=> (8-x)  ( (8-x)³  + (x² + 40 - 12x)(4-x) = 0

=> x = 8

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