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