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If x=7+4√3 , find the value …

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If x=7+4√3 , find the value of √x+1/√x

    • Posted by Tanya Negi 4 years, 2 months ago

    CBSE > Class 09 > Mathematics
    • 1 answers

    Nancy Singh 4 years, 2 months ago

    Given : x = 7 + 4√3 To find : √x + 1 / √x. Solution :  x = 7 + 4√3. ⇒ x = 4 + 3 + 4√3. ⇒ x = 2² + √3² + 2 × 2 × √3. ⇒ x = ( 2 + √3)² ⇒ √x = 2 + √3. Now, 1 /√x = 1 / 2 + √3 × 2 - √3 / 2 - √3. ⇒ 1 / √x = 2 - √3 / 2² - √3² ⇒ 1 / √x = 2 - √3 / 4 - 3. ⇒ 1 / √x = 2 - √3. Again, √x +1 / √x = 2 + √3 + 2 - √3. ⇒ √x + 1 / √x = 2 + 2.

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