Question 4

What will be the value of xy, if $$x^{2}+y^{2}=45$$ and $$x-y=5$$ ?

Solution

Given : $$x^{2}+y^{2}=45$$ ----------(i)

Also, $$x-y=5$$

Squaring both sides, we get :

=> $$(x-y)^2=(5)^2$$

=> $$x^2+y^2-2xy=25$$

Substituting value from equation (i),

=> $$45-2xy=25$$

=> $$2xy=45-25=20$$

=> $$xy=\frac{20}{2}=10$$

=> Ans - (A)

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