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Question :
Find the value (s) of m , when √m + 259 /√m = 44
Answer :
⇒ √m + 269 / √m = 44
Substituting √m = x in the above equation
⇒ x + 259 / x = 44
Multiplying every term by x
⇒ x( x ) + ( 259 / x )( x ) = 44x
⇒ x² + 259 = 44x
⇒ x² - 44x + 259 = 0
Splitting the middle term
⇒ x² - 37x - 7x + 259 = 0
⇒ x( x - 37 ) - 7( x - 37 ) = 0
⇒ ( x - 37 )( x - 7 ) = 0
⇒ x - 37 = 0 or x - 7 = 0
⇒ x = 37 or x = 7
When x = 37
⇒ √m = 37
Squaring on both sides
⇒ ( √m )² = 37²
⇒ m = 1369
When x = 7
⇒ √m = 7
Squaring on both sides
⇒ ( √m )² = 7²
⇒ m = 49
Therefore the value of m is either 1369 or 49.
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