Question

What number added to 1 gives its own square?​

Answer 1

Hello Dear,

◆ Answer -

x = (1+√5)/2 or x = (1-√5)/2

◆ Explaination -

Let x be the number which when added to 1 gives its own square.

x + 1 = x²

x² - x - 1 = 0

Comparing with standard form ax² + bx + c = 0,

a = 1

b = -1

c = -1

So now, solution would be -

x = [-b ± √(b²-4ac)] / 2a

x = [-(-1) ± √((-1)²-4×1×(-1))] / (2 × 1)

x = (1±√5)/2

Hence, answer is x = (1+√5)/2 or x = (1-√5)/2.

Thanks dear..

Answer 2

Answer -

x = (1+√5)/2 or x = (1-√5)/2

Step by step Explaination -

Let x be the number which when added to 1 gives its own square.

x + 1 = x²

x² - x - 1 = 0

Comparing with standard form ax² + bx + c = 0,

a = 1

b = -1

c = -1

So now, solution would be -

x = [-b ± √(b²-4ac)] / 2a

x = [-(-1) ± √((-1)²-4×1×(-1))] / (2 × 1)

x = (1±√5)/2

Therefore, the answer is x = (1+√5)/2 or x = (1-√5)/2.