Question

Prove that 4-2√7 is an irrational number, given that ✓7 is an irrational number.​

Answer 1

hope this helps you mate

Answer 2

4-2√7 is irrational number if given that ✓7 is an irrational number.​

Step-by-step explanation:

Assume  that  4-2√7 is an rational number

=> 4-2√7   = p/q

Squaring both sides

=> 16 + 2/7  - 4√7  = p²/q²

=>  - 4√7  = p²/q² - 16 - 2/7

=> √7 = (p²/q² - 16 - 2/7)/-4

=> √7 = (16 + 2/7  -p²/q²  )/4

=> √7 = 4  + 2/8  - p²/4q²

RHS = Rational

LHS = irrational ( as given that ✓7 is an irrational number)

=> LHS ≠ RHS

Hence our assumption is wrong

Hence  4-2√7 is not an rational number

=> 4-2√7 is irrational number

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