C-11-Q086mediumsingle_mcq

The proof of $\left(\dfrac{a+b}{b+c}\right)^2 = \dfrac{a^2+b^2}{b^2+c^2}$ given $a:b = b:c$ uses the substitution $b^2 = ac$ and the expansion—

a $(a+b)^2 = a^2 + 2ab + b^2$
b $(a-b)^2 = a^2 - 2ab + b^2$
c $a^3 + b^3 = (a+b)(a^2-ab+b^2)$
d $a^2 - b^2 = (a-b)(a+b)$

ব্যাখ্যা

Replacing $b^2$ with $ac$ in the right side and expanding the numerator with $(a+b)^2=a^2+2ab+b^2$ lets the terms factor and cancel to confirm the identity. The square-of-a-sum expansion is the key algebraic step.

এই অধ্যায়ের আরও প্রশ্ন

C-11-Q087If , then—
C-11-Q088If and are not mutually equal, the value of each ratio is—
C-11-Q089If , then equals—
C-11-Q090If are continued proportional, then
C-11-Q091If are continued proportional, then equals—
C-11-Q092Given , the value of is—
C-11-Q093If , then
C-11-Q094The solutions of Example 5, where , include—
C-11-Q095The condition in Example 5 ensures—
C-11-Q096By componendo-dividendo on , the next simplified form is—

Algebraic Ratio and Proportion — সব প্রশ্ন দেখুন (180টি) →

The proof of $\left(\dfrac{a+b}{b+c}\right)^2 = \dfrac{a^2+b^2}{b^2+c^2}$ given $a:b = b:c$ uses the substitution $b^2 = ac$ and the expansion—

(a+b)^2 = a^2 + 2ab + b^2

(a-b)^2 = a^2 - 2ab + b^2

a^3 + b^3 = (a+b)(a^2-ab+b^2)

a^2 - b^2 = (a-b)(a+b)

The proof of (a+bb+c)2=a2+b2b2+c2\left(\dfrac{a+b}{b+c}\right)^2 = \dfrac{a^2+b^2}{b^2+c^2}(b+ca+b​)2=b2+c2a2+b2​ given a:b=b:ca:b = b:ca:b=b:c uses the substitution b2=acb^2 = acb2=ac and the expansion—

ব্যাখ্যা

এই অধ্যায়ের আরও প্রশ্ন

The proof of (a+bb+c)2=a2+b2b2+c2\left(\dfrac{a+b}{b+c}\right)^2 = \dfrac{a^2+b^2}{b^2+c^2}(b+ca+b​)2=b2+c2a2+b2​ given a:b=b:ca:b = b:ca:b=b:c uses the substitution b2=acb^2 = acb2=ac and the expansion—

ব্যাখ্যা

এই অধ্যায়ের আরও প্রশ্ন

The proof of $\left(\dfrac{a+b}{b+c}\right)^2 = \dfrac{a^2+b^2}{b^2+c^2}$ given $a:b = b:c$ uses the substitution $b^2 = ac$ and the expansion—

The proof of $\left(\dfrac{a+b}{b+c}\right)^2 = \dfrac{a^2+b^2}{b^2+c^2}$ given $a:b = b:c$ uses the substitution $b^2 = ac$ and the expansion—