Question

if x^4 + 1 = 1297 AND y^2 - 1 = 2400, find y^2 - x^2

Answer 1

Given   (correct values)

• x⁴ + 1 = 1297
• y⁴ - 1 = 2400

To find

• y² - x²

Solution

• x⁴ + 1 = 1297
• x⁴ = 1296
• x⁴ = 6⁴

⇾ Bases are same equate the power

• x = 6

➝ The value of x is 6

• y⁴ - 1 = 2400
• y⁴ = 2401
• y⁴ = 7⁴

⇾ Bases are same equate the power

• y = 7

➝ The value of y is 7

To find

• y² - x²
• (y + x) (y - x)   (a² - b²) = (a + b) (a - b)
• (7 + 6) ( 7 - 6)
• (13)(1)
• 13

➝ The value of y² - x² is 13

Answer 2

x⁴ + 1 = 1297

y⁴ - 1 = 2400

To find

y² - x²

Solution

x⁴ + 1 = 1297

x⁴ = 1296

x⁴ = 6⁴

⇾ Bases are same equate the power

x = 6

➝ The value of x is 6

y⁴ - 1 = 2400

y⁴ = 2401

y⁴ = 7⁴

⇾ Bases are same equate the power

y = 7