if a and b are the roots of the equation 5x+17x+6,find the valu of 1/a²+1/b²
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~Explaination :-
If α,β are the zeroes of the equation.
⇒ 5x² + 17x + 6 = 0.
As we know that,
Sum of the zeroes of the quadratic equation.
⇒ α + β = -b/a.
⇒ α + β = -(17)/5. = -17/5.
Products of the zeroes of the quadratic equation.
⇒ αβ = c/a.
⇒ αβ = 6/5.
~Solution :-
⇒ 1/α² + 1/β².
⇒ β² + α²/α²β².
As we know that,
Formula of :
⇒ a² + b² = (a + b)² - 2ab.
Using this formula in equation, we get.
⇒ [α + β]² - 2αβ/(αβ)².
Put the values in the equation, we get.
⇒ [-17/5]² - 2[6/5]/(6/5)².
⇒ [289/25 - 12/5]/36/25.
⇒ [289 - 60/25]/36/25.
⇒ [229/25]/36/25.
⇒ 229/25 × 25/36.
⇒ 229/36.
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