Question

√7+ √5/ √7 - √5 = a + b √35 find the value of a and b​

Answer 1

Answer:

a = 6, b = 1

Step-by-step explanation:

Please see the attached image for steps.

Answer 2

Answer:

a = 6

b = 1

Step-by-step-explanation:

We have given that,

( √7 + √5 ) / ( √7 - √5 ) = a + b √35

We have to find the values of a and b.

Now,

( √7 + √5 ) / ( √7 - √5 ) = a + b √35

By multiplying and dividing LHS by ( √7 + √5 ), we get,

⇒ [ ( √7 + √5 ) / ( √7 - √5 ) ] * ( √7 + √5 ) / ( √7 + √5 ) = a + b √35

⇒ ( √7 + √5 ) ( √7 + √5 ) / ( √7 - √5 ) ( √7 + √5 ) = a + b √35

We know that,

( a + b ) ( a - b ) = a² - b²

⇒ ( √7 + √5 )² / [ ( √7 )² - ( √5 )² ] = a + b √35

We know that,

( a + b )² = a² + 2ab + b²

⇒ [ ( √7 )² + 2 * √7 * √5 + ( √5 )² ] / ( 7 - 5 ) = a + b √35

⇒ ( 7 + 2 √35 + 5 ) / 2 = a + b √35

⇒ ( 12 + 2 √35 ) / 2 = a + b √35

⇒ ( 12 / 2 ) + ( 2 √35 / 2 ) = a + b √35

⇒ 6 + √35 = a + b √35

⇒ 6 + 1 √35 = a + b √35

By comparing both sides, we get,

• a = 6

• b = 1