X-1, 2x-3,√5x+2 are the three sides of a right triangle and √5x+2 is hypotenuse then the value of x is
Answers
Solution :-
using pythagoras theorem we get,
→ (Base)² + (Perpendicular)² = (Hypotenuse)²
→ (x - 1)² + (2x - 3)² = (√5x + 2)²
→ x² - 2x + 1 + 4x² - 12x + 9 = 5x² + 4 + 4√5x
→ 5x² - 14x + 10 = 5x² + 4√5x + 4
→ 4√5x + 14x = 10 - 4
→ 2(2√5x + 7x) = 6
→ x(2√5 + 7) = 3
→ x = 3/(2√5 + 7)
→ x = {3/(2√5 + 7)} * {(2√5 - 7)/(2√5 - 7)}
→ x = 3(2√5 - 7)/{(2√5)² - 7²)
→ x = 3(2√5 - 7)/(20 - 49)
→ x = - {3(2√5 - 7)/29}
now, taking (-1) common from numerator of RHS,
→ x = {(21 - 6√5)/29} (Ans.)
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