Question

If x = √3 − √2 , find the value of ( −1 )square 2

Answer 1

Step-by-step explanation:

▪️Let √x - 1/√x = a

▪️Squaring both the sides,

▪️x + 1/x - 2 = a^2

▪️Putting the value,

▪️3–2√2 + 1/(3–2√2) - 2 = a^2

▪️a^2 = 1 - 2√2 + 1/(3–2√2)

▪️= [(3–2√2) (1–2√2) + 1] / 3–2√2

▪️= {3 - 8√2 + 9} / 3–2√2

▪️= [12 - 8√2] / 3–2√2

▪️Rationalising both the sides

▪️= {(12 - 8√2)(3+2√2)} ÷ (9–8)

▪️= 36 + 24√2 - 24√2 + 16(2)

▪️= 36 - 32

▪️=> 4

▪️a^2 = 4

▪️a = √4

▪️a = 2, -2

▪️So,

▪️√x - 1/√x = a = 2, -2.

Hopes it help you❤️❤️