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प्रश्न
Solve the following quadratic equations by factorization:
`3sqrt(5)x^2 + 25x - 10sqrt(5) = 0`
बेरीज
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उत्तर
Given: `3sqrt(5)x^2 + 25x - 10sqrt(5) = 0`
Step-wise calculation:
1. Try to factor into two binomials:
`(sqrt(5)x + 10)(3x - sqrt(5))`
2. Expand to check:
`(sqrt(5)x)(3x) + (sqrt(5)x)(-sqrt(5)) + 10(3x) + 10(-sqrt(5))`
= `3sqrt(5)x^2 - 5x + 30x - 10sqrt(5)`
= `3sqrt(5)x^2 + 25x - 10sqrt(5)`
3. Set each factor = 0:
`sqrt(5) x + 10 = 0`
⇒ `x = -10/sqrt(5)`
⇒ `x = -2sqrt(5)`
`3x - sqrt(5) = 0`
⇒ `x = sqrt(5)/3`
The solutions are `x = -2sqrt(5)` and `x = sqrt(5)/3`.
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