Question

The equation whose roots are 1/3+√2 and 1/3-√2 is

Answer 1

We have to find the quadratic equation whose roots are 1/(3 + √2) and 1/(3 - √2).

solution : roots of quadratic equation are 1/(3 + √2) and 1/(3 - √2).

sum of roots = 1/(3 + √2) + 1/(3 - √2)

= {(3 - √2) + (3 + √2)}/(3 + √2)(3 - √2)

= 6/(3² - √2²)

= 6/(9 - 2)

= 6/7

product of zeroes = 1/(3 + √2) × 1/(3 - √2)

= 1/{(3 + √2)(3 - √2)}

= 1/(3² - √2²)

= 1/(9 - 2)

= 1/7

now quadratic equation is x² - (sum of zeroes)x + product of zeroes = 0

⇒x² - (6/7)x + (1/7) = 0

⇒7x² - 6x + 1 = 0

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