1.

If a and b are the roots of the equation 5x+17x+6,find the valu of 1/a²+1/b²​

Answer»

ANSWER :

~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.

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~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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