Question

class 9 maths.....number system
answer is 24√2
need step by step explaination ​

Answer 1

Step-by-step explanation:

m= 1+√2

then 1/m = 1/(1+√2)

= {1(1-√2)}/{(1+√2)(1-√2)}. [ multiply with (1-√2) ]

= (1-√2)/ (1²-√2²)

= (1-√2)/(1-2)

= +1-√2)/-1

= -(1-√2)

= √2-1

m²+1/m²= (1+√2)²+(√2-1)²

= 1+2√2+2+2-2√2+1

= 6

m²-1/m²= (1+√2)²-(√2-1)²

= 1+2√2+2-2+2√2-1

= 4√2

then m⁴-1/m⁴

= (m²)²-(1/m²)²

= (m²+1/m²)(m²-1/m²)

= 6 × 4√2

= 24√2