DIESTRICTIONS TO CANDIDATESto the notice of the principal of thetied o

1.	DIESTRICTIONS TO CANDIDATESto the notice of the principal of thetied on the answer book The Red Noesponsibility of the candidatsanyat oDrove that ra trf is an irrinationaplomber.Books ietsAct No.the alla
Answer» To prove:√2+√7 is irrationalProof:Let is assume that √2+√7 is rational Thus√2 +√7 = a/b (where a and b are co-prime) √7 = a/b -√2 Squaring both sides a²/b² - 2√2a/b + 2 = 7a²/b² - 5 = 2√2a/b (a² - 5b²) / 2ab =√2 √2 is an irrational number . This contradicts the fact that√2 is irrational . So , our assumption is wrong.Hence , √2 +√7 is irrational

DIESTRICTIONS TO CANDIDATESto the notice of the principal of thetied on the answer book The Red Noesponsibility of the candidatsanyat oDrove that ra trf is an irrinationaplomber.Books ietsAct No.the alla

Answer»

To prove:√2+√7 is irrationalProof:Let is assume that √2+√7 is rational

Thus√2 +√7 = a/b (where a and b are co-prime)

√7 = a/b -√2

Squaring both sides

a²/b² - 2√2a/b + 2 = 7a²/b² - 5 = 2√2a/b

(a² - 5b²) / 2ab =√2

√2 is an irrational number .

This contradicts the fact that√2 is irrational .

So , our assumption is wrong.Hence , √2 +√7 is irrational