Question 68

If 2a + 3b = 8 and ab = 5, thenfind the value of $$4a^2 + 9b^2.$$

Solution

Given, $$2a+3b = 8$$ and $$ab = 5$$

$$=$$> $$\left(2a+3b\right)^2=8^2$$

$$=$$> $$4a^2+9b^2+2.2a.3b=64$$

$$=$$> $$4a^2+9b^2+12ab=64$$

$$=$$> $$4a^2+9b^2+12\left(5\right)=64$$

$$=$$> $$4a^2+9b^2=64-60$$

$$=$$> $$4a^2+9b^2=4$$

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